Boundary Integral Method for Thermoelastic Screen Scattering Problem in R

We investigate a three-dimensional mathematical thermoelastic scattering problem from an open surface which will be referred to as a screen. Under the assumption of the local "nite energy of the uni"ed thermoelastic scattered "eld, we give a weak model on the appropriate Sobolev spaces and derive equivalent integral equations of the "rst kind for the jump of some trace operators on the open surface. Uniqueness and existence theorems are proved, the regularity and the singular behaviour of the solution near the edge are established with the help of the Wiener}Hopf method in the halfspace, the calculus of pseudodi!erential operators on the basis of the strong ellipticity property and Gas rding's inequality. An improved Galerkin scheme is provided by simulating the singular behaviour of the exact solution at the edge of the screen. Copyright ( 2000 John Wiley & Sons, Ltd.