On a pseudoparabolic problem with constraint. (English) Zbl 1212.35261

Summary: This work deals with the study of a nonlinear degenerate pseudoparabolic problem. Arising from the modelling of sedimentary basin formation, the equation degenerates in order to take implicitly into account a constraint on the time derivative of the unknown. An existence result of a solution with an adapted compactness result and qualitative properties of the solutions are proposed (localization, finite speed of propagation, etc.).


35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35Q35 PDEs in connection with fluid mechanics
35R35 Free boundary problems for PDEs