Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method

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Abstract

In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of ℝN, with a measure as data and different boundary conditions: mixed, Neumann or Fourier. The first part is devoted to the proof of regularity results for solutions of convection-diffusion equations with these boundary conditions and data in (W1,q(Ω))&vprime;, when q <N/(N -1). The second part transforms, thanks to a duality trick, these regularity results into existence and uniqueness results when the data are measures.

Original languageEnglish
Pages (from-to)1341-1396
Number of pages56
JournalAdvances in Differential Equations
Volume5
Issue number10-12
Publication statusPublished - 1 Dec 2000
Externally publishedYes

Cite this

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title = "Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method",
abstract = "In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of ℝN, with a measure as data and different boundary conditions: mixed, Neumann or Fourier. The first part is devoted to the proof of regularity results for solutions of convection-diffusion equations with these boundary conditions and data in (W1,q(Ω))&vprime;, when q <N/(N -1). The second part transforms, thanks to a duality trick, these regularity results into existence and uniqueness results when the data are measures.",
author = "J{\'e}r{\^o}me Droniou",
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Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method. / Droniou, Jérôme.

In: Advances in Differential Equations, Vol. 5, No. 10-12, 01.12.2000, p. 1341-1396.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method

AU - Droniou, Jérôme

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N2 - In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of ℝN, with a measure as data and different boundary conditions: mixed, Neumann or Fourier. The first part is devoted to the proof of regularity results for solutions of convection-diffusion equations with these boundary conditions and data in (W1,q(Ω))&vprime;, when q <N/(N -1). The second part transforms, thanks to a duality trick, these regularity results into existence and uniqueness results when the data are measures.

AB - In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of ℝN, with a measure as data and different boundary conditions: mixed, Neumann or Fourier. The first part is devoted to the proof of regularity results for solutions of convection-diffusion equations with these boundary conditions and data in (W1,q(Ω))&vprime;, when q <N/(N -1). The second part transforms, thanks to a duality trick, these regularity results into existence and uniqueness results when the data are measures.

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EP - 1396

JO - Advances in Differential Equations

JF - Advances in Differential Equations

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