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EXISTENCE OF WEAK SOLUTIONS TO A NONLINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR SOURCES
2017 (English)In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, article id 202Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2017. article id 202
Identifiers
URN: urn:nbn:se:kau:diva-65859ISI: 000410390400001OAI: oai:DiVA.org:kau-65859DiVA: diva2:1177520
Available from: 2018-01-25 Created: 2018-01-25 Last updated: 2018-01-25

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CiteExportLink to record
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  • apa
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