Method of Monotone Solutions for Reaction-Diffusion Equations

V Volpert, V Vougalter
2017 Contemporary Mathematics. Fundamental Directions  
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
more » ... obtained for monotone solutions allowing to prove their existence by the LS method. Various applications of this method are given.
doi:10.22363/2413-3639-2017-63-3-437-454 fatcat:2yyu22nxfrec5kj4j6usjqwdei