Search

The present study is related to the existence and the asymptotic behavior of the solution of a nonlinear elliptic Steklov problem imposed on a nanostructure depending on the thickness parameter ε\varepsilon (nano-scale), distributed on the boundary of the domain when the parameter ε\varepsilon goes to 0, under some appropriate conditions on the data involved in the problem. We use epi-convergence method in order to establish the limit behavior by characterizing the weak limits of the energies for the solutions. An intermediate step in the proof provides a homogenization result for the considered structure.

A two-dimensional time dependent model of an interaction between a thin elastic plate and a Newtonian viscous fluid described by the non-steady Stokes equations is considered. It depends on a small parameter ε that is the ratio of the thicknesses of the plate and the fluid layer. The Young's modulus of the plate and its density may be great or small parameters equal to some powers (positive or negative) of ε while the density and the viscosity of the fluid are supposed to be of order one. An asymptotic expansion is constructed and justified for various magnitudes of the rigidity and density of the plate. The limit problems are studied in all these cases. They are Stokes equations with some special coupled or uncoupled boundary conditions modeling the interaction with the plate. The estimates of the difference between the exact solution and a truncated asymptotic expansion are established. These estimates justify the asymptotic approximations. [ABSTRACT FROM AUTHOR]

We propose a method of bi-coordinate variations for limit non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the cost function and parameters of the feasible set. It consists in making descent steps with respect to only two selected coordinates satisfying some special threshold rule. The method is simpler essentially than the usual gradient or dual type ones and differs from the previous known bi-coordinate ones suggested for the usual stationary and smooth problems. We establish its convergence under rather mild assumptions. Computational tests illustrate stable convergence properties of the proposed method. [ABSTRACT FROM AUTHOR]

The aim of this paper, is to study the limit behavior of the solution of a convex elasticity problem with negative power type, of a containing structure, an elastic thin oscillating layer of thickness depending of a small enough parameter. The epi-convergence method is considered to nd the limit problems with interface conditions.

A periodic, axially symmetric time-dependent model of interaction between a viscous fluid and a thin cylindrical elastic tube is considered. The problem depends on a small parameter , representing the ratio of the thickness of the wall and the radius of the cylinder. We consider Young's modulus of the elastic medium and its density great or small parameters equal to some powers of . An asymptotic expansion is constructed for various magnitudes of the rigidity and of the density of the elastic tube. The generality of the considered model requires to take into account six different combinations of the three parameters depending on . We obtain in this way different limit problems which are Stokes equations with some special boundary conditions. The expansion is justified by the high-order estimates for the difference of the exact solution and truncated asymptotic approximation. [ABSTRACT FROM AUTHOR]

In the present work, we study the asymptotic behavior of solutions to a plasticity problem in a containing structure, a thin plastic plate of thickness that tends to zero. To find the limit problems with interface conditions we use the epiconvergence method.

In the present work, we study the asymptotic behavior of solutions to a plasticity problem in a containing structure, a thin plastic plate of thickness that tends to zero. To find the limit problems with interface conditions we use the epiconvergence method. [ABSTRACT FROM AUTHOR]

We analyze the exponential decay property of solutions of the semilinear wave equation in bounded domain Ω of R N with a damping term which is effective on the exterior of a ball and boundary conditions of the Cauchy-Ventcel type. Under suitable and natural assumptions on the nonlinearity, we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p < 5. The results obtained in R 3 and R N by B. Dehman, G. Lebeau and E. Zuazua on the inequalities of the classical energy (which estimate the total energy of solutions in terms of the energy localized in the exterior of a ball) and on Strichartz’s estimates, allow us to give an application to the stabilization controllability of the semilinear wave equation in a bounded domain of R N with a subcritical nonlinearity on the domain and its boundary, and conditions on the boundary of Cauchy-Ventcel type. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we show that, under suitable assumptions, the solutions to the approximating initial and boundary value problems (cf. introduction) converge in , for suitable indexes and , to the solution to the limit problem . The last two Sections 4–5 are devoted to a similar approximation result, in a Banach-space framework, and involve a generalization of the kernels k, h and operator A. [Copyright &y& Elsevier]

A partial analogy exists between the lifespan neuropsychological development of individuals and the biological evolution of species: In both of these major categories of growth, progressive emergence of wholes transcends inherently limited part-processes. The remarkably small purview of each moment of consciousness experienced by an individual may be a crucial aspect of maintaining organization in that individual's cognitive development, protecting it from combinatorial chaos. In this essay I summarize experimental psychology research showing that working memory capacity comprises the so-called magical number 7±2 items, not only for words and digits but for spatial items and other sorts of cognitive materials, and not only in humans but also in other species. This is so to such an extent that 7±2 may be a“constant of nature.” The small quantity range 7±2 independent items, which builds upon a more elementary, instantaneous working memory capacity of three or four items, is surprisingly independent of the time duration of a cognitive task. Moreover, it is largely independent of ontogeny. Explanations of these powerful facts about working memory are offered here within both a functionalistic framework and a framework of hypothetical neural processes. At the neural level, working memory dynamics may comprise certain brain wave harmonics or topological relationships in the sheetlike cortex. Within the functionalistic framework, I suggest an additional analogy, pertaining to cultural evolution, with Tom Gilbert's work on risk analysis and“the global problematic” that follows from unforeseen consequences of the expansiveness of human ambition. Several connections are drawn with ideas presented by participants in the Chicago Religion and Science Group about how theologies and sciences try to understand the possibility of adaptive exercises of human freedom in the face of the extreme finiteness of each human individual. [ABSTRACT FROM AUTHOR]

We consider the ordinary differential equation of the second order, which describes oscillations of a satellite with respect to its mass center moving along an elliptic orbit with eccentricity e. The equation has two parameters: e and µ. It is regular for 0 ≤ e < 1 and singular when e = 1. For $$e \to $$ 1 we obtain three limit problems. Their bounded solution to the first limit problem form a two-dimensional (2D) continuous invariant set with a periodic structure. Solutions to the second limit problem form 2D and 3D manifolds. The µ-depending families of odd bounded solutions are singled out. One of the families is twisted into a self-similar spiral. To obtain the limit families of the periodic solutions to the original problem match together the odd bounded solutions to the first and the second limit problem. The point of conjunction is described by the third (the basic) limit problem. The limit families are very close to prelimit ones computed in earlier studies. [ABSTRACT FROM AUTHOR]