Vanishing non-local regularization of a scalar conservation law

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)

Abstract

We prove that the solution to the regularization of a scalar conservation law by a fractional power of the Laplacian converges, as the regularization vanishes, to the entropy solution of the hyperbolic problem. We also give an error estimate when the initial condition has bounded variation.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalElectronic Journal of Differential Equations
Volume2003
Publication statusPublished - 28 Nov 2003
Externally publishedYes

Keywords

  • Error estimate
  • Fractal operator
  • Scalar conservation law
  • Vanishing regularization

Cite this

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title = "Vanishing non-local regularization of a scalar conservation law",
abstract = "We prove that the solution to the regularization of a scalar conservation law by a fractional power of the Laplacian converges, as the regularization vanishes, to the entropy solution of the hyperbolic problem. We also give an error estimate when the initial condition has bounded variation.",
keywords = "Error estimate, Fractal operator, Scalar conservation law, Vanishing regularization",
author = "J{\'e}r{\^o}me Droniou",
year = "2003",
month = "11",
day = "28",
language = "English",
volume = "2003",
pages = "1--20",
journal = "Electronic Journal of Differential Equations",
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publisher = "Texas State University, Department of Mathematics",

}

Vanishing non-local regularization of a scalar conservation law. / Droniou, Jérôme.

In: Electronic Journal of Differential Equations, Vol. 2003, 28.11.2003, p. 1-20.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Vanishing non-local regularization of a scalar conservation law

AU - Droniou, Jérôme

PY - 2003/11/28

Y1 - 2003/11/28

N2 - We prove that the solution to the regularization of a scalar conservation law by a fractional power of the Laplacian converges, as the regularization vanishes, to the entropy solution of the hyperbolic problem. We also give an error estimate when the initial condition has bounded variation.

AB - We prove that the solution to the regularization of a scalar conservation law by a fractional power of the Laplacian converges, as the regularization vanishes, to the entropy solution of the hyperbolic problem. We also give an error estimate when the initial condition has bounded variation.

KW - Error estimate

KW - Fractal operator

KW - Scalar conservation law

KW - Vanishing regularization

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M3 - Article

VL - 2003

SP - 1

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JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

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