On wave equations with boundary dissipation of memory type

Abstract

The undamped wave equation on an open domain of arbitrary dimension and boundary of class C1 is considered. On parts of the boundary the normal derivative of the solution equals the convolution of its time derivative with a measure of positive type. This setting subsumes standard dissipative boundary conditions as well as the interaction with viscoelastic boundary materials. Applying methods for evolutionary integral equations to a variational formulation of the problem, existence, uniqueness and regularity of the solution to the wave equation is proven under minimal regularity assumptions on the initial conditions and forcing functions. To evaluate the versatility of a parametrized model, least-squares fits to physical data are presented. © 1996 Rocky Mountain Mathematics Consortium.