Two-dimensional riemann problem for a single conservation law

Tong Zhang, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

The entropy solutions to the partial differential equation (∂/∂t)u(t, x, y) + (∂/∂x)f(u(t, x, y)) + (∂/∂y)g(u(t, x, y)) = 0, with initial data constant in each quadrant of the (x, y) plane, have been constructed and are piecewise smooth under the condition f"(u) ≠ 0, g"(u) ≠ 0, (f"(u)lg"(u))' ≠ 0. This problem generalizes to several space dimensions the important Riemann problem for equations in one-space dimension. Although existence and uniqueness of solutions are well known, little is known about the qualitative behavior of solutions. It is this with which we are concerned here.

Original languageEnglish (US)
Pages (from-to)559-619
Number of pages61
JournalTransactions of the American Mathematical Society
Volume312
Issue number2
DOIs
StatePublished - Apr 1989

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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