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The paper is devoted to a problem of acquiring elastic properties of a composite material from the vibration testing data with a simplified experimental acquisition scheme. The specimen is considered to abide by the linear elasticity laws and subject to viscoelastic damping. The boundary value problem for transverse movement of such a specimen in the frequency domain is formulated and solved with finite-element method. The correction method is suggested for the finite element matrices to account for the mass of the accelerometer. The problem of acquiring the elastic parameters is then formulated as a nonlinear least-square optimization problem. The usage of the automatic differentiation technique for stable and efficient computation of the gradient and hessian allows to use well-studied first and second order local optimization methods. We also explore the possibility of generating initial guesses for local minimization by heuristic global methods. The results of the numerical experiments on simulated data are analyzed in order to provide insights for the following real life experiments. [ABSTRACT FROM AUTHOR]

In this paper we study a partial inverse spectral problem for non-self-adjoint Sturm–Liouville operators with a constant delay and show that subspectra of two boundary value problems with one common boundary condition are sufficient to determine the complex potential. We developed the Horváth's method in [M. Horváth, On the inverse spectral theory of Schrödinger and Dirac operators, Trans. Amer. Math. Soc. 353 2001, 10, 4155–4171] for the self-adjoint Sturm–Liouville operator without delay into the non-self-adjoint Sturm–Liouville differential operator with a constant delay. [ABSTRACT FROM AUTHOR]

In this paper, a Sturm–Liouville boundary value problem which includes conformable fractional derivatives of order α, 0 < α ≤ 1 {0<\alpha\leq 1} is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra and classical spectral data. We also study the half-inverse problem and prove a Hochstadt–Lieberman-type theorem. [ABSTRACT FROM AUTHOR]

Consider the interior transmission problem arising in inverse boundary value problems for the diffusion equation with discontinuous diffusion coefficients. We prove the unique solvability of the interior transmission problem by constructing its Green function. First, we construct a local parametrix for the interior transmission problem near the boundary in the Laplace domain, by using the theory of pseudo-differential operators with a large parameter. Second, by carefully analyzing the analyticity of the local parametrix in the Laplace domain and estimating it there, a local parametrix for the original parabolic interior transmission problem is obtained via the inverse Laplace transform. Finally, using a partition of unity, we patch all the local parametrices and the fundamental solution of the diffusion equation to generate a global parametrix for the parabolic interior transmission problem and then compensate it to get the Green function by the Levi method. The uniqueness of the Green function is justified by using the duality argument, and then the unique solvability of the interior transmission problem is concluded. We would like to emphasize that the Green function for the parabolic interior transmission problem is constructed for the first time in this paper. It can be applied for active thermography and diffuse optical tomography modeled by diffusion equations to identify an unknown inclusion and its physical property. [ABSTRACT FROM AUTHOR]

Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method. [ABSTRACT FROM AUTHOR]

In the recent paper [Colombo, Physica D 236: 81–89, 2007] the author investigates an inverse problem arising in the theory of combustion. The problem studied is: determine the temperature u and the convolution memory kernel k in the evolution equation given suitable initial-boundary conditions and the following additional restriction on u: ∫Ω φ( x) u( t, x) dx = g( t), where φ and g are given functions. The main results are a local in time existence theorem and a global in time uniqueness result. In this paper we complete the study considering the linearized version of the model. We prove that, if F( u( t, x), ∇ u( t, x)) is sublinear, then the inverse problem has a unique global in time solution. [ABSTRACT FROM AUTHOR]

This paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg-de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhgeĭm-Klibanov method. [ABSTRACT FROM AUTHOR]

In this paper, the criterion of resolvability of the inverse problem of heat conduction is established. [ABSTRACT FROM AUTHOR]

In this paper we investigate the identification of the time-dependent perfusion coefficient in the transient bio-heat conduction equation. Apart from the usual initial and Dirichlet/Neumann boundary conditions, in this inverse coefficient identification problem the additional measurement information to render a unique solution is represented by the time history of a heat flux/boundary temperature. Several necessary and sufficient conditions for the existence and uniqueness of the solution are provided. [ABSTRACT FROM AUTHOR]

In the present paper, the inverse problem with unknown composite right-hand side for second-order linear hyperbolic equations is examined. Solution existence, uniqueness, and stability for the boundary-value problem are established. [ABSTRACT FROM AUTHOR]