On a nonlinear hyperbolic variational equation: II. The zero-viscosity and dispersion limits

John K. Hunter, Yuxi Zheng

Research output: Contribution to journalArticle

39 Scopus citations

Abstract

We consider viscosity and dispersion regularizations of the nonlinear hyperbolic partial differential equation (ut+uux)x=1/2ux2 with the simplest initial data such that ux blows up in finite time. We prove that the zero-viscosity limit selects a unique global weak solution of the partial differential equation without viscosity. We also present numerical experiments which indicate that the zero-dispersion limit selects a different global weak solution of the same initial-value problem.

Original languageEnglish (US)
Pages (from-to)355-383
Number of pages29
JournalArchive for Rational Mechanics and Analysis
Volume129
Issue number4
DOIs
StatePublished - Dec 1 1995

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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