Optimal tracing of viscous shocks in solutions of viscous conservation laws

Wen Shen, Rea Park Mee

Research output: Contribution to journalArticle

Abstract

This paper contains a qualitative study of a scalar conservation law with viscosity: ut + f(u)x = uxx. We consider the problem of identifying the location of viscous shocks, thus obtaining an optimal finite dimensional description of solutions to the viscous conservation law. We introduce a nonlinear functional whose minimizers yield the viscous traveling profiles which optimally fit the given solution. We prove that outside an initial time interval and away from times of shock interactions, our functional remains very small, i.e., the solution can be accurately represented by a finite number of viscous traveling waves.

Original languageEnglish (US)
Pages (from-to)1474-1488
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume38
Issue number5
DOIs
StatePublished - Dec 1 2006

Fingerprint

Viscous Conservation Laws
Tracing
Shock
Conservation
Scalar Conservation Laws
Minimizer
Traveling Wave
Viscosity
Interval
Interaction

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Optimal tracing of viscous shocks in solutions of viscous conservation laws. / Shen, Wen; Mee, Rea Park.

In: SIAM Journal on Mathematical Analysis, Vol. 38, No. 5, 01.12.2006, p. 1474-1488.

Research output: Contribution to journalArticle

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