A filtration model with hysteresis
The author proves the existence of a time global solution for a quasi-variational formulation of a parabolic equation modeling a filtration phenomena taking account of hysteresis effects. In particular, he shows the existence of an almost everywhere solution. The hysteresis relationship is described by a ``perturbation'' of a generalized play operator. Moreover the model is intended for an unsaturated flow of a compressible fluid through a porous medium, and the describing equation is linear in its second order part. The proof of the existence makes use of a fixed point procedure, and of a sophisticated technique previously exploited by the author and collaborators. Hysteresis in filtration phenomena brings interesting application and mathematical problems. On such a subject, see for instance the works by the present reviewer and A. Visintin.
scientific article; zbMATH DE number 2104527
scientific article