Electron. J. Differential Equations, Vol. 2019 (2019), No. 70, pp. 1-19.

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

Gleiciane da Silva Aragao, Flank David Morais Bezerra

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.

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Gleiciane da Silva Aragão
Departamento de Ciências Exatas e da Terra
Universidade Federal de São Paulo
Av. Conceição, 515, Centro, Cep 09920-000
Diadema-SP, Brazil
email: gleiciane.aragao@unifesp.br, Phone +55 (11) 4044-0500
Flank David Morais Bezerra
Departamento de Matemática
Universidade Federal da Paraíba
Cidade Universitária, Campus I
Via Expressa Padre Zé-Castelo Branco III, Cep 58051-900
João Pessoa-PB, Brazil
email: flank@mat.ufpb.br, Phone +55 (83) 3216-7434

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