Gleiciane da Silva Aragao, Flank David Morais Bezerra
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.
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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 |
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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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