A strongly degenerate system involving an equation of parabolic type and an equation of elliptic type |
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| Authors: | Xiangsheng Xu |
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| Affiliation: | Department of Mathematical Sciences , University of Arkansas , Fayetteville, 72701, Arkansas |
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| Abstract: | Abstract We show the existence of weak solutions in an elliptic region in the self-similar plane to the two-dimensional Riemann problem for the pressure-gradient system of the compressible Euler system. The two-dimensional Riemann problem we study is the interaction of two forward rarefaction waves, which are adjacent to a common vacuum that occupies a sectorial domain of 90 degrees. We assume the origin is on the boundary of the domain. In addition, the domain is open, bounded, and simply connected with a piecewise C 2,α boundary. We resolve the difficulty that arises from the fact that the origin is on the boundary of the domain. |
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