On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations

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dc.contributor.authorHolden, Helge
dc.contributor.authorKarlsen, Kenneth H.
dc.contributor.authorRisebro, Nils H.
dc.date.accessioned2020-11-20T18:38:30Z
dc.date.available2020-11-20T18:38:30Z
dc.date.issued2003-04-22
dc.description.abstractWe prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general Lp compactness criterion. The uniqueness proof is an adaptation of Kružkov's "doubling of variables" proof. We also present a numerical example motivated by biodegradation in porous media.
dc.description.departmentMathematics
dc.formatText
dc.format.extent31 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationHolden, H., Karlsen, K. H., & Risebro, N. H. (2003). On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. <i>Electronic Journal of Differential Equations, 2003</i>(46), pp. 1-31.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/12983
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear degenerate parabolic equations
dc.subjectWeakly coupled systems
dc.subjectEntropy solution
dc.subjectUniqueness
dc.subjectExistence
dc.subjectFinite difference method
dc.titleOn uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations
dc.typeArticle

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