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On equations of Benjamin–Bona–Mahony type

2004; Elsevier BV; Volume: 59; Issue: 8 Linguagem: Inglês

10.1016/j.na.2004.08.013

1873-5215

J. Límaco, H. R. Clark, L. A. Medeiros,

Differential Equations and Boundary Problems

The objective of this paper is to establish existence, uniqueness and regularity of solutions for a mixed problem associated with equations of Benjamin–Bona–Mahony type in a domain Q^ with moving boundary. The technique, to show the existence of solutions, consists in transforming Q^ into a cylinder Q by using a diffeomorphism Tt and to apply in Q the Faedo–Galerkin method in the transformed mixed problem. The uniqueness of solutions is proved by using the energy method in the non-cylindrical domain Q^.