Method of Monotone Solutions for Reaction-Diffusion Equations

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Abstract

Existence of solutions of reaction-diffusion systems of equations in unbounded domains is studied by the Leray-Schauder (LS) method based on the topological degree for elliptic operators in unbounded domains and on a priori estimates of solutions in weighted spaces. We identify some reactiondiffusion systems for which there exist two subclasses of solutions separated in the function space, monotone and non-monotone solutions. A priori estimates and existence of solutions are obtained for monotone solutions allowing to prove their existence by the LS method. Various applications of this method are given.

About the authors

V Volpert

Institut Camille Jordan, UMR 5208 CNRS, University Lyon; INRIA Team Dracula, INRIA Lyon La Doua; RUDN University

Email: volpert@math.univ-lyon1.fr
1, 69622 Villeurbanne, France; 69603 Villeurbanne, France;6 Miklukho-Maklaya st., 117198 Moscow, Russia

V Vougalter

University of Toronto

Email: volpert@math.univ-lyon1.fr
Toronto, M5S 2E4 Ontario, Canada

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