Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 08, pp. 1-18.
Title: Dissipative Boussinesq equations on non-cylindrical
domains in R^n
Authors: Haroldo R. Clark (Univ. Federal Fluminense, Brazil)
Alfredo T. Cousin (Univ. Estadual de Maringa, Brazil)
Cicero L. Frota (Univ. Estadual de Maringa, Brazil)
Juan Limaco (Univ. Federal Fluminense, Brazil)
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.