Large time behavior and homogenization of solutions of two‐dimensional conservation laws

Bjorn Engquist, E. Weinan

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We study the large time behavior of solutions of scalar conservation laws in one and two space dimensions with periodic initial data. Under a very weak nonlinearity condition, we prove that the solutions converge to constants as time goes to infinity. Even in one space dimension our results improve the earlier ones since we only require the fluxes to be nonlinear in a neighborhood of the mean value of the initial data. We then use these results to study the homogenization problem for scalar conservation laws with oscillatory initial data.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalCommunications on Pure and Applied Mathematics
Volume46
Issue number1
DOIs
StatePublished - Jan 1 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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