A SPACE-TIME VARIATIONAL FORMULATION FOR THE BOUNDARY INTEGRAL-EQUATION IN A 2D ELASTIC CRACK PROBLEM

This paper investigates the transient elastic wave scattering by a crack in R2 by means of Boundary Integral Equation Method. The analysis of the Laplace-Fourier transform (in time) of the integral operator allows to obtain existence, uniqueness and continuity dependence of the solution with respect to the data, in a Sobolev functional framework. A regularisation of the hypersingular BIE is applied in order to remove the hypersingularity and to write the associated time-space variational formulation on a tractable form. A Galerkin-type approximation is then performed to solve this variational formulation and we finally present some numerical results.