Clark, Haroldo R.; Cousin, Alfredo T.; Frota, Cícero L.; Límaco, Juan Dissipative Boussinesq equations on non-cylindrical domains in \(\mathbb R^n\). (English) Zbl 1184.35054 Electron. J. Differ. Equ. 2010, Paper No. 08, 18 p. (2010). Summary: 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. MSC: 35B40 Asymptotic behavior of solutions to PDEs 35Q35 PDEs in connection with fluid mechanics Keywords:time dependent domains; existence; uniqueness; initial-boundary value problem PDF BibTeX XML Cite \textit{H. R. Clark} et al., Electron. J. Differ. Equ. 2010, Paper No. 08, 18 p. (2010; Zbl 1184.35054) Full Text: EMIS