Stability of viscous scalar shock fronts in several dimensions

Jonathan Goodman

Research output: Contribution to journalArticle

Abstract

We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.

Original languageEnglish (US)
Pages (from-to)683-695
Number of pages13
JournalTransactions of the American Mathematical Society
Volume311
Issue number2
DOIs
StatePublished - 1989

Fingerprint

Equations of motion
Shock
Conservation
Scalar
Viscous Conservation Laws
Scalar Conservation Laws
Motion
Energy Estimates
Nonlinear Stability
Term

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Stability of viscous scalar shock fronts in several dimensions. / Goodman, Jonathan.

In: Transactions of the American Mathematical Society, Vol. 311, No. 2, 1989, p. 683-695.

Research output: Contribution to journalArticle

@article{6efc28cce9e0425e9012658fe8cfd8fa,
title = "Stability of viscous scalar shock fronts in several dimensions",
abstract = "We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the {"}integrated equation{"} and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.",
author = "Jonathan Goodman",
year = "1989",
doi = "10.1090/S0002-9947-1989-0978372-9",
language = "English (US)",
volume = "311",
pages = "683--695",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "2",

}

TY - JOUR

T1 - Stability of viscous scalar shock fronts in several dimensions

AU - Goodman, Jonathan

PY - 1989

Y1 - 1989

N2 - We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.

AB - We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.

UR - http://www.scopus.com/inward/record.url?scp=33646885643&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646885643&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1989-0978372-9

DO - 10.1090/S0002-9947-1989-0978372-9

M3 - Article

AN - SCOPUS:33646885643

VL - 311

SP - 683

EP - 695

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -