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Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Universit√° Giustino Fortunato, Italy .
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
2017 (English)In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, Vol. 2017, no 202, p. 1-16Article 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
San Marcos: Texas State University , 2017. Vol. 2017, no 202, p. 1-16
Keywords [en]
Reaction-diffusion systems, singular parabolic equations, weak solutions
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-63606ISI: 000410390400001OAI: oai:DiVA.org:kau-63606DiVA, id: diva2:1140653
Available from: 2017-09-12 Created: 2017-09-12 Last updated: 2020-04-14Bibliographically approved

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Muntean, Adrian

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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Language
  • de-DE
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  • en-US
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  • nn-NB
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Output format
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