Search

Abstract: In (2012), Leonetti and Siepe [10] considered solutions to boundary value problems of some anisotropic elliptic equations of the type Under some suitable conditions, they obtained an integrability result, which shows that higher integrability of the boundary datum forces solutions to have higher integrability as well. In the present paper, we consider -obstacle problems of the nonhomogeneous anisotropic elliptic equations under some controllable growth and monotonicity conditions. We obtain an integrability result, which can be regarded as a generalization of the result due to Leonetti and Siepe. [Copyright &y& Elsevier]

This paper deals with the chemotaxis–haptotaxis system with signal-dependent sensitivity { u t = Δ u − ∇ ⋅ ( χ ( v ) u ∇ v ) − ξ ∇ ⋅ ( u ∇ w ) + μ u ( 1 − u − w ) , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , w t = − v w , x ∈ Ω , t > 0 under homogeneous Neumann boundary conditions and initial conditions, where Ω ⊂ R n ( n ≥ 3 ) is a bounded domain with smooth boundary, ξ , μ > 0 are constants and χ is a function satisfying some conditions. In the case that χ is a constant it is known that the above system possesses a global classical solution under some conditions (Cao [4] , Tao [10] , Tao and Winkler [11] ); however, in the case that χ is a function, the above system has not been studied. The purpose of this paper is to establish global existence and boundedness in the above system. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following Keller–Segel–Navier–Stokes system (⋆) { n t + u ⋅ ∇ n = Δ n − ∇ ⋅ ( n S ( x , n , c ) ∇ c ) , x ∈ Ω , t > 0 , c t + u ⋅ ∇ c = Δ c − c + n , x ∈ Ω , t > 0 , u t + κ ( u ⋅ ∇ ) u = Δ u + ∇ P + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 , where Ω ⊂ R 3 is a bounded domain with smooth boundary ∂ Ω , κ ∈ R and S denotes a given tensor-valued function fulfilling | S ( x , n , c ) | ≤ C S ( 1 + n ) α with some C S > 0 and α > 0 . As the case κ = 0 has been considered in [25] , it is shown in the present paper that the corresponding initial–boundary problem with κ ≠ 0 admits at least one global weak solution if α ≥ 3 7 . [ABSTRACT FROM AUTHOR]

Abstract Geometric gradient flows for elastic energies of Willmore type play an important role in mathematics and in many applications. The evolution of elastic curves has been studied in detail both for closed as well as for open curves. Although elastic flows for networks also have many interesting features, they have not been studied so far from the point of view of mathematical analysis. So far it was not even clear what are appropriate boundary conditions at junctions. In this paper we give a well-posedness result for Willmore flow of networks in different geometric settings and hence lay a foundation for further mathematical analysis. A main point in the proof is to check whether different proposed boundary conditions lead to a well posed problem. In this context one has to check the Lopatinskii–Shapiro condition in order to apply the Solonnikov theory for linear parabolic systems in Hölder spaces which is needed in a fixed point argument. We also show that the solution we get is unique in a purely geometric sense. [ABSTRACT FROM AUTHOR]

Let B denote the unit ball in RN with boundary S. For a non-negative C2 subharmonic function f on B and ∈S, we define the Lusin square area integral Sα(,f) by Sα(f)=[Γα(1-|x|)2-NΔf2(x)dx]12,where for α>1, Γα={x∈B:|x-|<α(1-|x|)} is the non-tangential approach region at ∈S, and Δ is the Laplacian in RN. In the paper we will prove the following: Let f be a non-negative subharmonic function such thatfpois subharmonic for somepo>0. Iffpp=sup0po, then for everyα>1,Sα(•,f)p≤Aα,pfpfor some constantAα,pindependent of f. The above result includes the known results for harmonic or holomorphic functions in the Hardy Hp spaces, as well as for a system F=(u1,...,uN) of conjugate harmonic functions for which it is known that |F|p=(Σuj2)p/2 is subharmonic for p≥(N-2)/(N-1),N≥3. We also consider analogues of the functions g and g\* of Littlewood-Paley, and introduce the function gλ\*, λ>1, defined bygλ\*(,f)=[B(1-|y|)Δf2(y)Kλ(y,)dy]12,whereKλ(y,)=(1-|y|)(λ-1)(N-1)|y-|λ(N-1). In the paper we prove that the inequality gλ\*(•,f)p≤Cpfp holds for all λ≥N/(N-1) when p≥2, and for λ>3-p whenever 1(2N-3)/(N-1). [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the hyperbolic–parabolic mixed type equations with the non-homogeneous boundary condition. If it is degenerate on the boundary, the part of the boundary whose boundary value should be imposed, is determined by the entropy condition from the convection term. If there is no convection term in the equation, we show that the stability of solutions can be proved without any boundary condition. If the equation is completely degenerate, we show that the stability of solutions can be established just based on the partial boundary condition. [ABSTRACT FROM AUTHOR]

This paper studies the nonisotropic chaotic oscillations of the initial-boundary value problem of one-dimensional wave equation with a mixing transport term. It separately considers that the boundary condition at the right-end of the wave equation is a superlinear type and linear perturbation of such type, each causing the total energy of the underlying system to rise and fall due to the interaction with a mixing transport term. For each type of boundary condition, the occurrence of nonisotropic chaotic oscillations is rigorously proved. Numerical examples verify the effectiveness of theoretical prediction. [ABSTRACT FROM AUTHOR]

The inverse spectral problem for a Sturm–Liouville problem which consists of a Sturm–Liouville equation defined on the interval [ 0 , a ] and two separated boundary conditions at the endpoints 0 and a , one of which is involved function f ( λ ) , is considered in this paper. When f ( λ ) is the type of Herglotz functions and is known as a priori, we prove that the potential on [ 0 , a ] and the other boundary condition can be uniquely determined in terms of appropriate partial information on the spectrum and partial information on the set of normalizing constants. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonexistences of positive solutions for the following two mixed boundary value problems. The first problem is the nonlinear-Neumann mixed boundary value problem { − Δ u = f ( u ) in R + N , ∂ u ∂ ν = g ( u ) on Γ 1 , ∂ u ∂ ν = 0 on Γ 0 and the second is the nonlinear-Dirichlet mixed boundary value problem { − Δ u = f ( u ) in R + N , ∂ u ∂ ν = g ( u ) on Γ 1 , u = 0 on Γ 0 , where N ≥ 3 , R + N = { x ∈ R N : x N > 0 } , Γ 1 = { x ∈ R N : x N = 0 , x 1 < 0 } and Γ 0 = { x ∈ R N : x N = 0 , x 1 > 0 } . We will prove that these problems possess no positive solution under some assumptions on the nonlinear terms. The main method we use is the moving plane method in an integral form. [ABSTRACT FROM AUTHOR]

The Berry heuristic has been a long standing ansatz about the high energy (i.e. large eigenvalues) behaviour of eigenfunctions (see [7] ). Roughly speaking, it states that under some generic boundary conditions, these eigenfunctions exhibit Gaussian behaviour when the eigenvalues grow to infinity. Our aim in this paper is to make this statement quantitative and to establish some rigorous bounds on the distance to Gaussianity, focussing on the hyperspherical case (i.e., for eigenfunctions of the Laplace–Beltrami operator on the normalized d -dimensional sphere – also known as spherical harmonics). Some applications to non-Gaussian models are also discussed. [ABSTRACT FROM AUTHOR]

In this short note, we revisit the blow-up of solution for the initial boundary value problem of semilinear pseudo-parabolic equations with low/critical initial energy stated in Xu and Su (2013) [4] , and amend the proofs of the original paper. [ABSTRACT FROM AUTHOR]

In this paper we give an existence theorem of global classical solution to the initial boundary value problem for the quasilinear parabolic equations of divergence form u t − div { σ ( | ∇ u | 2 ) ∇ u } = f ( ∇ u , u , x , t ) where σ ( | ∇ u | 2 ) may not be bounded as | ∇ u | → ∞ . As an application the logarithmic type nonlinearity σ ( | ∇ u | 2 ) = log ⁡ ( 1 + | ∇ u | 2 ) which is growing as | ∇ u | → ∞ and degenerate at | ∇ u | = 0 is considered under f ≡ 0 . [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the quasilinear fully parabolic Keller–Segel system under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary, . The diffusivity is assumed to satisfy some further technical conditions such as algebraic growth and , which says that the diffusion is allowed to be not only non-degenerate but also degenerate. The global-in-time existence and uniform-in-time boundedness of solutions are established under the subcritical condition that for with , and . When , this paper represents an improvement of Tao and Winkler [17], because the domain does not necessarily need to be convex in this paper. In the case and , uniform-in-time boundedness is an open problem left in a previous paper [7]. This paper also gives an answer to it in bounded domains. [Copyright &y& Elsevier]

In this paper an immersed boundary method with semi-implicit fluid–solid coupling for mobile particles of arbitrary density ratio is developed. The new scheme does not require any iterations to balance fluid forces and particle forces at the interface. A new formulation of the particle equations of motion is proposed which not only accounts for the particle itself but also for a Lagrangian layer surrounding the particle surface. Furthermore, it is shown by analytical considerations that the six equations for the linear and angular velocity of the spherical particle decouple which allows their sequential solution. On this basis a new time integration scheme is obtained which is unconditionally stable for all fluid–solid density ratios and enables large time steps, with Courant numbers around unity. The new scheme is extensively validated for various test cases and its convergence is assessed. An appealing issue is that compared to existing immersed boundary methods the new scheme only alters coefficients in the particle equations and the order of the steps, making it easy to implement in present codes with explicit coupling. This substantially extends the field of application of such methods. [ABSTRACT FROM AUTHOR]

In this paper we consider a one-dimensional free boundary problem describing adsorption phenomena in a porous media. This problem was already proposed and we established a local existence in time and a uniqueness result in [1,4] . Here, through the discussion for the dynamics of the free boundary in wetting and drying processes we suppose a specific form of the growth rate condition for the free boundary. By using this form in our problem we can obtain the global existence of a solution in time and convergence of the free boundary as t → ∞ . [ABSTRACT FROM AUTHOR]

In this paper we will show that monomial summability processes with respect to different monomials are not compatible, except in the (trivial) case of a convergent series. We will apply this fact to the study of solutions of Pfaffian systems with normal crossings, focusing in the implications of the complete integrability condition on these systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a reaction–diffusion–advection equation with a free boundary which models the spreading of an invasive species in one-dimensional heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. Investigating the sign of the principal eigenvalue of the associated linearized eigenvalue problem, under certain conditions we obtain the sharp criteria for spreading and vanishing via system parameters. Also, we establish the long-time behavior of the solution and the asymptotic spreading speed. Finally, some biological implications are discussed. [ABSTRACT FROM AUTHOR]

This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value problem in a bounded domain by using an exact transparent boundary condition. The well-posedness and stability of the solution are established for the reduced problem. Moreover, a priori energy estimates are obtained with minimum regularity requirement for the data and explicit dependence on the time. [ABSTRACT FROM AUTHOR]

This paper is concerned with the renormalized stochastic entropy solutions of stochastic scalar conservation law forced by a multiplicative noise on a bounded domain with a non-homogeneous boundary condition. We first introduce a notion of renormalized stochastic entropy solutions and then establish the existence and uniqueness of the renormalized stochastic entropy solutions for a general L 1 -data. Our results allow us to give a positive answer to an open problem posed by Bauzet, Vallet and Wittbold in [4] . [ABSTRACT FROM AUTHOR]

In this paper, when the initial density has a jump across an interior curve in a bounded domain, we show unique existence, piecewise regularity and jump discontinuity dynamics for the density and the velocity vector governed by the Navier–Stokes equations of compressible viscous barotropic flows. A critical difficulty is in controlling the gradient of the pressure across the jump curve. This is resolved by constructing a vector function associated with the pressure jump value on the convecting curve and extending it to the whole domain. [ABSTRACT FROM AUTHOR]

Abstract: The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to study the qualitative behavior of large solutions to the following problem Here is a positive function with , is a non-negative function and may be singular near the boundary or vanish on the boundary, and the nonlinear term f is a Γ-varying function, whose variation at infinity is not regular. We focus our investigation on the existence and asymptotic behavior close to the boundary ∂Ω of large solutions by Karamata regular variation theory and the method of upper and lower solution. The main results of this paper emphasize the central role played by the gradient term and the weight functions and . [Copyright &y& Elsevier]

Abstract: With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the accuracy aspects of local ABCs designed for the scalar anisotropic wave equation in the frequency domain (time harmonic case). The ABC analyzed in this paper is the perfectly matched discrete layers (PMDL). PMDL is a simple variant of perfectly matched layers (PML) and is equivalent to rational approximation-based local ABCs. Specifically, we derive a sufficient condition for PMDL to accurately absorb wave modes with outgoing group velocities and this condition turns out to be a simple bound on the PMDL parameters. The reflection coefficient derived in this paper clearly reveals that the PMDL absorption is based on group velocities, and not phase velocities, and hence a PMDL can be designed to correctly identify and accurately absorb all outgoing wave modes (even those with opposing signs of phase and group velocities). The validity of the sufficient condition is demonstrated through a series of frequency domain simulations. In part 2 of this paper [S. Savadatti, M.N. Guddati, Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling, J. Comput. Phys. (2010), doi:10.1016/j.jcp.2010.05.017], the accuracy condition presented here is shown to govern both the well-posedness and accuracy aspects of PMDL designed for transient (time-dependent) modeling of scalar waves in anisotropic media. [ABSTRACT FROM AUTHOR]

Abstract: This paper mainly concerns Beurling type quotient modules of over the bidisk. By establishing a theorem of function theory over the bidisk, it is shown that a Beurling type quotient module is essentially normal if and only if the corresponding inner function is a rational inner function having degree at most . Furthermore, we apply this result to the study of boundary representations of Toeplitz algebras over quotient modules. It is proved that the identity representation of is a boundary representation of in all nontrivial cases. This extends a result of Arveson to Toeplitz algebras on Beurling type quotient modules over the bidisk (cf. [W. Arveson, Subalgebras of -algebras, Acta Math. 123 (1969) 141–224; W. Arveson, Subalgebras of -algebras II, Acta Math. 128 (1972) 271–308]). The paper also establishes K-homology defined by Beurling type quotient modules over the bidisk. [Copyright &y& Elsevier]

Abstract: In this paper, the multiplicity of Lagrangian orbits on smooth compact symmetric star-shaped hypersurfaces with respect to the origin in is studied. These Lagrangian orbits begin from one Lagrangian subspace and end on another. An infinitely many existence result is proved via -index theory. This is a multiplicity result about the Arnold Chord Conjecture in some sense, and is a generalization of the problem about the multiplicity of Lagrangian orbits beginning from and ending on the same Lagrangian subspace which was considered in the authors'' previous paper [F. Guo, C. Liu, Multiplicity of Lagrangian orbits on symmetric star-shaped hypersurfaces, Nonlinear Anal. 69 (4) (2008) 1425–1436]. [Copyright &y& Elsevier]

Abstract: In the beginning of the 1990s we devoted a sequence of papers to perturbation theory, singular limits and well-posedness problems. In particular, the strong well-posedness of the initial–boundary value problem for the compressible Euler equations was demonstrate for the first time. Our method also allowed singular limit results in the strong norm, even under assumptions weaker than the current ones in the literature (where the strong norm is not reached). It is worth noting that, until now, the above method and results have not been substantially improved. Hence an introduction to it still looks timely. Actually, in a forthcoming paper, by returning to this method, we improve (in a very substantial way) some important results recently appeared in the literature. [Copyright &y& Elsevier]

Abstract: In the paper, a maximum principle for the generalized time-fractional diffusion equation over an open bounded domain is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Caputo–Dzherbashyan fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial-boundary-value problem for the generalized time-fractional diffusion equation possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions. [Copyright &y& Elsevier]

Abstract: We revisit the study in [Y. Trakhinin, On the existence of incompressible current-vortex sheets: study of a linearized free boundary value problem, Math. Methods Appl. Sci. 28 (2005) 917–945] where an energy a priori estimate for the linearized free boundary value problem for planar current-vortex sheets in ideal incompressible magnetohydrodynamics was proved for a part of the whole stability domain found a long time ago in [S.I. Syrovatskij, The stability of tangential discontinuities in a magnetohydrodynamic medium, Zh. Eksper. Teor. Fiz. 24 (1953) 622–629 (in Russian); W.I. Axford, Note on a problem of magnetohydrodynamic stability, Canad. J. Phys. 40 (1962) 654–655]. In this paper we derive an a priori estimate in the whole stability domain. The crucial point in deriving this estimate is the construction of a symbolic symmetrizer for a nonstandard elliptic problem for the small perturbation of total pressure. This symmetrizer is an analogue of Kreiss'' type symmetrizers. As in hyperbolic theory, the failure of the uniform Lopatinski condition, i.e., the fact that current-vortex sheets are only weakly (neutrally) stable yields loss of derivatives in the energy estimate. The result of this paper is a necessary step to prove the local-in-time existence of stable nonplanar incompressible current-vortex sheets by a suitable Nash–Moser type iteration scheme. [Copyright &y& Elsevier]

Abstract: We show in this paper that the -groups governing neutron transport equations with reflecting boundary conditions in slab geometry satisfy a weak spectral mapping theorem in any spaces . The main part of this paper is dealing with collisionless transport -group while the full transport -group is dealt with by stability arguments. [Copyright &y& Elsevier]

Abstract: In this paper, several existence theorems of positive solutions are established for nonlinear m-point boundary value problem for p-Laplacian dynamic equations on time scales, as an application, an example to demonstrate our results is given. The conditions we used in the paper are different from those in [H.R. Sun, W.T. Li, Positive solutions for nonlinear three-point boundary value problems on time scales, J. Math. Anal. Appl. 299 (2004) 508–524; H.R. Sun, W.T. Li, Positive solutions for nonlinear m-point boundary value problems on time scales, Acta Math. Sinica 49 (2006) 369–380 (in Chinese); Y. Wang, C. Hou, Existence of multiple positive solutions for one-dimensional p-Laplacian, J. Math. Anal. Appl. 315 (2006) 144–153; Y. Wang, W. Ge, Positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian, Nonlinear Appl. 66 (6) (2007) 1246–1256]. [Copyright &y& Elsevier]

Abstract: This paper proposes a hybrid method for the prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the power flow analysis (PFA) algorithm and statistical energy analysis (SEA) coupling concepts. The main part of this method is the application of the coupling loss factor (CLF) of SEA to the boundary condition of PFA in reverberant system. First, for hybrid PFA, the hybrid boundary conditions on 1-D and 2-D cases were derived in the general form. To verify the derived boundary conditions, numerical analyses for each case were performed. The hybrid PFA solutions using derived boundary conditions were compared with the classical PFA solutions with various reverberance factors including the effects of the characteristic length, excitation frequency and group velocity besides damping loss factor of the subsystem. Additionally, the hybrid PFA on 3-D case and the hybrid power flow finite element method (PFFEM) for hybrid PFA of built-up structures are described in the other companion paper. [Copyright &y& Elsevier]

Abstract: The paper deals with canard solutions at very general turning points of smooth singular perturbation problems in two dimensions. We follow a geometric approach based on the use of -normal forms, centre manifolds and (family) blow up, as we did in (Trans. Amer. Math. Soc., to appear). In (Trans. Amer. Math. Soc., to appear) we considered the existence of manifolds of canard solutions for given appropriate boundary conditions. These manifolds need not be smooth at the turning point. In this paper we essentially study the transition time along such manifolds, as well as the divergence integral, providing a structure theorem for these integrals. As a consequence we get a nice structure theorem for the transition equation, governing the canard solutions. It permits to compare different control manifolds and to obtain a precise description of the entry–exit relation of different canard solutions. Attention is also given to the special case in which the canard manifolds are smooth, i.e. when “formal” canard solutions exist. [Copyright &y& Elsevier]

Abstract: The paper is aimed as a contribution to the general theory of nonlinear infinite dimensional dynamical systems describing interacting physiologically structured populations. We carry out continuation of local solutions to maximal solutions in a functional analytic setting. For maximal solutions we establish global existence via exponential boundedness and by a contraction argument, adapted to derive uniform existence time. Moreover, within the setting of dual Banach spaces, we derive results on continuous dependence with respect to time and initial state. To achieve generality the paper is organized top down, in the way that we first treat abstract nonlinear dynamical systems under very few but rather strong hypotheses and thereafter work our way down towards verifiable assumptions in terms of more basic biological modelling ingredients that guarantee that the high level hypotheses hold. [Copyright &y& Elsevier]

In this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non-locally reacting boundary. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the global structure of radial positive solutions of boundary value problem div ( ϕ N ( ∇ v ) ) + λ f ( | x | , v ) = 0 in B ( R ) , v = 0 on ∂ B ( R ) , where ϕ N ( y ) = y 1 − | y | 2 , y ∈ R N , λ is a positive parameter, B ( R ) = { x ∈ R N : | x | < R } , and | ⋅ | denotes the Euclidean norm in R N . All results, depending on the behavior of nonlinear term f near 0, are obtained by using global bifurcation techniques. [ABSTRACT FROM AUTHOR]

In this paper we consider the following system involving more than two competitive populations of biological species all of which are attracted by the same chemoattractant. { u 1 t = Δ u 1 − χ 1 ∇ ⋅ ( u 1 ∇ w ) + μ 1 u 1 ( 1 − ∑ i = 1 n a 1 i u i ) , x ∈ Ω , t > 0 , u 2 t = Δ u 2 − χ 2 ∇ ⋅ ( u 2 ∇ w ) + μ 2 u 2 ( 1 − ∑ i = 1 n a 2 i u i ) , x ∈ Ω , t > 0 , ⋯ ⋯ u n t = Δ u n − χ n ∇ ⋅ ( u n ∇ w ) + μ n u n ( 1 − ∑ i = 1 n a n i u i ) , x ∈ Ω , t > 0 , − Δ w + λ w = ∑ i = 1 n u i , x ∈ Ω , t > 0 , under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R N ( N ≥ 1 ) with smooth boundary. We prove that if μ i , χ i and the following matrix A = ( a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋮ ⋱ ⋮ a n 1 a n 2 ⋯ a n n ) satisfy certain properties, then all solutions of this system will stabilize towards a positive equilibrium { u i ⁎ } i = 1 , … , n which is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Monge–Ampère equation det D 2 u ( x ) = b ( x ) f ( u ( x ) ) , x ∈ Ω , where Ω is a strictly convex, bounded smooth domain in R N with N ≥ 2 , and b ∈ C ∞ ( Ω ¯ ) which is positive in Ω, but may be vanishing on the boundary. We find a new structure condition on f which plays a crucial role in the boundary behavior of strictly convex large solutions. Our results are obtained in a more general setting than those in Cîrstea and Trombetti (2008) [12] , where f is regularly varying at infinity with index p > N . [ABSTRACT FROM AUTHOR]

In this paper, we focus on the dynamics for a Lotka–Volterra type weak competition system with two free boundaries, where free boundaries which may intersect each other as time evolves are used to describe the spreading of two competing species, respectively. In the weak competition case, the dynamics of this model can be classified into four cases, which forms a spreading–vanishing quartering. The notion of the minimal habitat size for spreading is introduced to determine if species can always spread. Some sufficient conditions for spreading and vanishing are established. Also, when spreading occurs, some rough estimates for spreading speed and the long-time behavior of solutions are established. [ABSTRACT FROM AUTHOR]

In this paper, we study the initial–boundary value problem of viscoelastic equations with coupled nonlinear boundary conditions. By using the energy perturbation method, we establish decay results of the solution as time goes to infinity. [ABSTRACT FROM AUTHOR]

This paper presents an integral equation approach for pricing American continuous-installment options when the stock price follows Heston's stochastic volatility model. By exploiting a log-linear relationship of the free boundary function with respect to volatility changes and using the decomposition technique and Fourier inversion transform, we drive integral expressions of the initial premium along with the optimal stopping and early exercise boundaries for this option. This offers a system of nonlinear Volterra integral equations for determining the two free boundaries, which can be used to estimate the option price. Numerical integration technique accompanied with the Newton–Rahpson iteration procedure is proposed for solving the integral equations. The method is implemented, and some numerical examples are provided to examine the boundary properties and the option price behavior. The computational efficiency of this method is also considered. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the global regularity for solutions of the -Laplacian in two-dimensional convex domains with Dirichlet boundary conditions. Here with and . [Copyright &y& Elsevier]

This paper is addressed to studying the exact controllability of stochastic Schrödinger equations by two controls. One is a boundary control and the other is an internal control in the diffusion term. By means of the duality argument, the control problem is converted into an observability problem for backward stochastic Schrödinger equations, and the desired observability estimate is obtained by a global Carleman estimate. At last, we give a result about the lack of exact controllability, which shows that the action of two controls is necessary. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the Cauchy problem of the periodic two-component hyperelastic-rod wave equation. We first establish the local well-posedness and precise blow-up scenario. Then we obtain several blow-up results and the blowup rate of strong solutions. Moreover, we present two global existence results for strong solutions. Finally, we consider analyticity of solutions and the initial–boundary value problem. [Copyright &y& Elsevier]

Abstract: This paper presents an experimental procedure for the axial load identification of slender prismatic beams with unknown boundary conditions by making use of one vibration frequency and of five amplitudes of the corresponding mode shape. In fact, this method does not require the knowledge of the effective length of the beam under examination, but only the flexural rigidity and mass per unit length. The proposed algorithm was verified by means of many numerical and experimental tests on tie-rods having different boundary conditions. Excellent estimates of the axial forces were obtained. Finally, the influence of the location of the instrumented sections on the estimation of the axial load was analyzed using a simply supported beam model. [Copyright &y& Elsevier]

Abstract: We consider the following heat equation with nonlinear boundary conditions: in , on . This equation admits positive -axial symmetric steady states if and only if . In this paper, we study the stability of those positive -axial symmetric steady states for the case . [Copyright &y& Elsevier]

Abstract: Let be the unit ball centered at the origin in . In this paper we study the following problem where , . We prove that for any , if is small enough, the above problem has a positive solution concentrating at distinct points tending to the boundary of as goes to . [Copyright &y& Elsevier]

Abstract: This paper is concerned with a competitive and cooperative mathematical model for two biological populations which dislike crowding, diffuse slowly and live in a common territory under different kind of intra- and inter-specific interferences. The model consists of a system of two doubly nonlinear parabolic equations with nonlocal terms and Neumann boundary conditions. Based on the theory of the Leray–Schauder degree, we obtain the coexistence periodic solutions, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two interacting populations, under different intra- and inter-specific interferences on their natural growth rates. [Copyright &y& Elsevier]

Abstract: In this paper, we consider invariant subspaces of operators in the class , which is the set of operators such that and commute. It is shown that every operator in the class such that the outer boundary of its spectrum is the outer boundary of a Carathéodory domain has a nontrivial invariant subspace. We also give a family of operators in the class which are reductive, i.e., their invariant subspaces are reducing. In addition, we give a condition on spectra of operators in the class which gives some information about invariant subspaces. [Copyright &y& Elsevier]

Abstract: This paper investigates the inverse problem of finding a time-dependent coefficient in a heat equation with nonlocal boundary and integral overdetermination conditions. Under some regularity and consistency conditions on the input data, the existence, uniqueness and continuous dependence upon the data of the solution are shown by using the generalized Fourier method. [Copyright &y& Elsevier]

Abstract: In this paper we establish a comparison result through symmetrization for solutions to some boundary value problems involving the fractional Laplacian. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of suitable radial problems. Furthermore, we use such result to prove a priori estimates for solutions in terms of the data, providing several regularity results which extend the well-known ones for the classical Laplacian. [Copyright &y& Elsevier]