Semi-hyperbolic patches of solutions of the pressure gradient system

Kyungwoo Song, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


We construct patches of self-similar solutions, in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves, to the two-dimensional pressure gradient system. This type of solutions is common in the solutions of two-dimensional Riemann problems, as seen from numerical experiments. They are not determined by the hyperbolic domain of determinacy in the traditional sense. They are middle-way between the fully hyperbolic (supersonic) and elliptic region, which we call semi-hyperbolic or partially hyperbolic. Our intention is to use the patches as building tiles to construct global solutions to general Riemann problems.

Original languageEnglish (US)
Pages (from-to)1365-1380
Number of pages16
JournalDiscrete and Continuous Dynamical Systems
Issue number4
StatePublished - Aug 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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