The Lax solution to a Hamilton-Jacobi equation and its generalizations: Part 2

Ya V. Mykytiuk, A. K. Prykarpatsky, D. Blackmore

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A study on the Lax solution to a Hamilton-Jacobi equation is presented. It is proved that the function defined by the infimum-based Lax formula provides a solution almost everywhere in x for each fixed t>0 to the Hamilton-Jacobi, Cauchy problem. A generalization of the Lax formula is developed for the more inclusive Hamilton-Jacobi equation.

Original languageEnglish (US)
Pages (from-to)629-640
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Volume55
Issue number5
DOIs
StatePublished - Nov 1 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • F set
  • Hamilton-Jacobi equation
  • Lax formula
  • Lebesgue measure
  • Semicontinuity
  • Viscosity solution

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