On the asymptotic behaviour for an electromagnetic system with a dissipative boundary condition
Giovambattista Amendola · IMA Journal of Applied Mathematics · 2004
In this work we study some properties of solutions for the system describing a three-dimensional non-homogeneous non-conducting dielectric with a general boundary condition with memory. We first show the existence of the inverse of this boundary condition, which allows us to introduce a boundary free energy, similar to the one considered by Fabrizio & Morro (1996, Arch. Rat. Mech. Anal., 136, 359–381). Then, we prove existence and uniqueness theorems for weak and strong solutions of the evolutive problem in a finite time interval. Moreover, following Rivera & Olivera (1997, Boll. U.M.I., 11-A, 115–127), we examine some dissipative properties of the boundary condition and of its inverse and we give a useful energy estimate. Finally, when there is no memory in the boundary condition the exponential decay of the solution is proved.