Electron. J. Diff. Equ., Vol. 2010(2010), No. 08, pp. 1-18.

Dissipative Boussinesq equations on non-cylindrical domains in R^n

Haroldo R. Clark, Alfredo T. Cousin, Cicero L. Frota, Juan Limaco

Abstract:
This article concerns the initial-boundary value problem for the nonlinear Boussinesq equations on time dependent domains in $\mathbb{R}^n$ with $1\leq n \leq 4$. Global solvability, uniqueness of solutions and the exponential decay to the energy are established provided the initial data are bounded in some sense.

Submitted September 13, 2009. Published January 16, 2010.
Math Subject Classifications: 35L10, 35Q53, 35B40.
Key Words: Boussinesq equation; time dependent domains; existence; uniqueness; asymptotic behavior.

Show me the PDF file (284 KB), TEX file, and other files for this article.

Haroldo R. Clark
Universidade Federal Fluminense
IM-GAN, RJ, Brasil
email: hclark@vm.uff.br
Alfredo T. Cousin
Universidade Estadual de Maringá
DMA, PR, Brasil
email: atcousin@uem.br
Cícero Lopes Frota
Universidade Estadual de Maringá
DMA, PR, Brasil
email: clfrota@uem.br
Juan Límaco
Universidade Federal Fluminense
IM-GAN, RJ, Brasil
email: jlimaco@vm.uff.br

Return to the EJDE web page