November  2009, 24(4): 1365-1380. doi: 10.3934/dcds.2009.24.1365

Semi-hyperbolic patches of solutions of the pressure gradient system

1. 

Department of Mathematics, Kyung Hee University, Seoul 130-701, South Korea

2. 

Department of Mathematics, The Pennsylvania State University, PA 16802

Received  June 2008 Revised  December 2008 Published  May 2009

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.
Citation: Kyungwoo Song, Yuxi Zheng. Semi-hyperbolic patches of solutions of the pressure gradient system. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1365-1380. doi: 10.3934/dcds.2009.24.1365
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