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We prove an existence theorem for the anisotropic, time-harmonic poro-elastic boundary value problem by using the Gårding inequality. [ABSTRACT FROM AUTHOR]

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of the central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical fluid-structure interaction problem by using a coupling procedure that reduces the problem to a nonlocal initial-boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time-dependent fluid-structure interaction problems by convolution quadrature coupling of FEM and BEM. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We reduce an exterior initial boundary value problem for the wave equation in three space dimensions to an initial boundary value problem on a bounded computational domain bounded by an artificial boundary as well as the original boundary. From a Kirchhoff representation formula for the solution of wave equation in an exterior domain, we derive on the artificial boundary (exact) transparent boundary conditions that are nonlocal in space and time. These lead to local approximate transparent boundary conditions of the first and second orders. It is shown that these approximate transparent conditions are satisfied exactly for a related spherically symmetric problem. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with a dual-mixed formulation for a three dimensional exterior Stokes problem via boundary integral equation methods. Here velocity, pressure and stress are the main unknowns. Following a similar analysis given recently for the Laplacian, we are able to extend the classical Johnson & Nédélec procedure to the present case, without assuming any restrictive smoothness requirement on the coupling boundary, but only Lipschitz-continuity. More precisely, after using the incompressibility condition to eliminate the pressure, we consider the resulting velocity-stress approach with a Neumann boundary condition on an annular bounded domain, and couple the underlying equations with only one boundary integral equation arising from the application of the normal trace to the Green representation formula in the exterior unbounded region. As a result, we obtain a saddle point operator equation, which is then analyzed by the wellknown Babuška-Brezzi theory: in particular, the well-posedness of the formulation will be established. [ABSTRACT FROM AUTHOR]