On equations of Benjamin–Bona–Mahony type Original Research Article

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 View the MathML sourceQ^ with moving boundary. The technique, to show the existence of solutions, consists in transforming View the MathML sourceQ^ into a cylinder Q by using a diffeomorphism TtTt 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 View the MathML source