Attractors in Models of Porous Media Flow

A. V. Akhmetzyanov^a^,*, A. G. Kushner^a^,^b^,**, and V. V. Lychagin^a^,^c^,***
Translated by I. Ruzanova

^aTrapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia

^bFaculty of Physics, Moscow State University, Moscow, 119992 Russia

^cUniversity of Tromsø, Tromsø, Norway

Correspondence to: * e-mail: atlas@ipu.ru
Correspondence to: ** e-mail: kushner@physics.msu.ru
Correspondence to: *** e-mail: valentin.lychagin@matnat.uit.no

Received 17 October, 2016

Abstract—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.

DOI: 10.1134/S1064562417010239