MULTI-PARAMETER PERTURBATIONS FOR THE SPACE-PERIODIC HEAT EQUATION

Abstract

We consider the acoustic field scattered by a bounded impenetrable obsta- cle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation ∆u + k2u = 0. We show that the solution u and its far field pattern u∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.