Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 70, pp. 1-19.

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

Authors: Gleiciane da Silva Aragao (Univ. Federal de Sao Paulo, Brazil)
         Flank David Morais Bezerra (Univ. Federal da Paraiba, Brazil)

Abstract:
 In this article we study 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  collapses toward
 the boundary as a parameter approaches zero. We prove the continuity
 of the set of equilibria for these equations. Moreover, if an equilibrium
 solution of the limit problem is hyperbolic, then we show that the perturbed
 equation has only one equilibrium solution nearby.

Submitted July 5, 2018. Published May 15, 2019.
Math Subject Classifications: 35L05, 35J61, 70K42, 37B55.
Key Words: Wave equation; semilinear elliptic equations; equilibria;
           non-autonomous; continuity; concentrating terms.