Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

Date

2017-09-06

Authors

de Bonis, Ida
Muntean, Adrian

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i) the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii) the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

Description

Keywords

Reaction-diffusion systems, Singular parabolic equations, Weak solutions

Citation

de Bonis, I., & Muntean, A. (2017). Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources. Electronic Journal of Differential Equations, 2017(202), pp. 1-16.

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Attribution 4.0 International

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