Attractors in models of porous media flow
Atlas V. Akhmetzyanov, Alexei Kushner, Valentin Lychagin · Doklady Mathematics · 2017
A constructive method is proposed for finding finite-dimensional submanifolds in the space of smooth functions that are invariant with respect to flows defined by evolutionary partial differential equations. Conditions for the stability of these submanifolds are obtained. Such submanifolds are constructed for generalized Rapoport–Leas equations that arise in the theory of porous media flows.