Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary

Abstract

In this paper we are interested in the behavior of the solutions of non-autonomous damped wave equations when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter \varepsilon goes to zero. We prove the conti- nuity of the set equilibria of these equations. Moreover, if an equilibrium solution of the limit problem is hyperbolic, then we show that the per- turbed equation has one and only one equilibrium solution nearby.