Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data

Jerome Droniou, Alain Prignet

Research output: Contribution to journalArticleResearchpeer-review

43 Citations (Scopus)

Abstract

We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded subset of R-N with Dirichlet homogeneous boundary conditions. The initial condition is in L-1 and the right hand side is a smooth measure. We extend a previous notion of entropy solutions and prove that they coincide with the renormalized solutions.
Original languageEnglish
Pages (from-to)181 - 205
Number of pages25
JournalNodea-Nonlinear Differential Equations and Applications
Volume14
Issue number1-2
DOIs
Publication statusPublished - 2007
Externally publishedYes

Cite this

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abstract = "We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded subset of R-N with Dirichlet homogeneous boundary conditions. The initial condition is in L-1 and the right hand side is a smooth measure. We extend a previous notion of entropy solutions and prove that they coincide with the renormalized solutions.",
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Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data. / Droniou, Jerome; Prignet, Alain.

In: Nodea-Nonlinear Differential Equations and Applications, Vol. 14, No. 1-2, 2007, p. 181 - 205.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Droniou, Jerome

AU - Prignet, Alain

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AB - We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded subset of R-N with Dirichlet homogeneous boundary conditions. The initial condition is in L-1 and the right hand side is a smooth measure. We extend a previous notion of entropy solutions and prove that they coincide with the renormalized solutions.

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