On the piewise smooth solutions to non-homogeneous scalar conservation laws

Yan Xiang Kan, Tao TANG*, Zhen Huan Teng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise smooth entropy solution along the generalized characteristics. These estimates play important roles in obtaining the optimal rate of convergence for various approximation methods to conservation laws.

Original languageEnglish
Pages (from-to)27-50
Number of pages24
JournalJournal of Differential Equations
Volume175
Issue number1
DOIs
Publication statusPublished - 1 Sep 2001

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Generalized characteristics
  • Non-homogeneous conservation laws
  • Piecewise smooth solution
  • Shock

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