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

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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