On the dissipative Boussinesq equation in a non-cylindrical domain

We investigate the initial–boundary value problem for the one-dimensional nonlinear Boussinesq equation inside domains with moving ends having both small increasing and decreasing displacements. Global solvability, uniqueness of solutions and the exponential decay to the energy are established provi...

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Veröffentlicht in:	Nonlinear analysis 2007-10, Vol.67 (8), p.2321-2334
Hauptverfasser:	Clark, H.R., Cousin, A.T., Frota, C.L., Límaco, J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Boussinesq equation Exact sciences and technology Existence Mathematical analysis Mathematics Non-cylindrical domains Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Sciences and techniques of general use Uniqueness and asymptotic behavior
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Beschreibung
Zusammenfassung:	We investigate the initial–boundary value problem for the one-dimensional nonlinear Boussinesq equation inside domains with moving ends having both small increasing and decreasing displacements. Global solvability, uniqueness of solutions and the exponential decay to the energy are established provided the initial data are bounded in some sense.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2006.09.009