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Journal Articles Journal of Mathematical Sciences Year : 2021

Method of Monotone Solutions for Reaction-Diffusion Equations

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 reaction-diffusion systems for which there exist two subclasses of solutions separated in the function space, monotone and nonmonotone 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.
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Dates and versions

hal-03398980 , version 1 (26-10-2021)

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Vitaly Volpert, Vitali Vougalter. Method of Monotone Solutions for Reaction-Diffusion Equations. Journal of Mathematical Sciences, 2021, 253, pp.660 - 675. ⟨10.1007/s10958-021-05260-2⟩. ⟨hal-03398980⟩
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