Electron. J. Diff. Equ., Vol. 2014 (2014), No. 243, pp. 1-14.

A mixed problem for semilinear wave equations with acoustic boundary conditions in domains with non-locally reacting boundary

Cicero L. Frota, Luiz A. Medeiros, Andre Vicente

Abstract:
In this article we study the existence, uniqueness and asymptotic stability of solution to the mixed problem for the semilinear wave equation with acoustic boundary conditions in domains with non-locally reacting boundary. We also prove the existence and uniqueness of solution to a problem with nonmonotone dissipative term.

Submitted July 14, 2014. Published November 18, 2014.
Math Subject Classifications: 35B40, 35L05.
Key Words: Nonlinear wave equation; non-locally reacting boundary; acoustic boundary conditions; nonlinear boundary condition; stabilization.

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Cícero L. Frota
Universidade Estadual de Maringá
- DMA. Av. Colombo, 5790, CEP: 87020-900
Maringá, PR, Brazil
email: clfrota@uem.br
Luiz A. Medeiros
Universidade Federal do Rio de Janeiro
- IM. Av. Athos da Silveira Ramos 149
CT, Cidade Universitária
CEP: 21941-909, Rio de Janeiro, RJ, Brazil
email: luizadauto@gmail.com
André Vicente
Universidade Estadual do Oeste do Paraná
- CCET, Rua Universitária, 2069
Jd. Universitário CEP: 85819-110,
Cascavel, PR, Brazil
email: andre.vicente@unioeste.br

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