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An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By applying a boundary-field equation method, we are able to formulate a nonlocal boundary problem (NBP) in the Laplace transformed domain, using the field equations inside the obstacle and boundary integral equations in the exterior elastic medium. Existence, uniqueness and stability of the solutions to the NBP are established in Sobolev spaces for two different integral representations. The corresponding results in the time domain are obtained. The stability bounds are translated into time domain estimates that can serve as the starting point for a numerical discretization based on Convolution Quadrature. [ABSTRACT FROM AUTHOR]

This paper is concerned with the application of time-domain boundary integral methods to a nonstationary boundary value problem for the thermo-elasto-dynamic equations, based on the Lubich approach via the Laplace transform. Fundamental solutions of the transformed thermo-elasto-dynamic equations are constructed explicitly by the Hörmander method. Simpleand double-layer potential boundary integral operators are introduced in the transformed domain, and their coercivity is established. Based on the estimates of various boundary integral operators in the transformed domain, existence and uniqueness results of solutions are established in the time domain. These results may serve as a mathematical foundation for the semidiscretization and full-discretization schemes based on the boundary element method and the convolution quadrature method for time domain boundary integral equations arising in thermoelasticity [ABSTRACT FROM AUTHOR]

This paper is concerned with boundary integral equation methods for solving the two-dimensional uid-solid interaction problem. We reduce the problem to three different systems of boundary integral equations via direct and indirect approaches. Existence and uniqueness results for variational solutions of boundary integral equations are established. Since in all these variational formulations, the hypersingular boundary integral operator associated with the time-harmonic Navier equation is a dominating integral operator, we also include a new regularization formulation for this hypersingular operator, which allows us to treat the hypersingular kernel by a weakly singular kernel. Numerical examples are presented to verify and validate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. This paper gives an overview of the method from both theoretical and numerical point of view. It summarizes the main results obtained by the author and his collaborators over the last 30 years. Fundamental theory and various applications will be illustrated through simple examples. Some numerical experiments in elasticity as well as in fluid mechanics will be included to demonstrate the efficiency of the methods. [Copyright &y& Elsevier]

This article is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green's formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different parts of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spaces. [ABSTRACT FROM AUTHOR]

Addresses the problem of estimation in the numerical solution of integral equations that arise in electromagnetics. Integral representations; Irregular frequencies; Calderon projectors; Finite energy and function spaces; Mapping properties; Residual errors; The perfectly conducting sphere; Conclusions.