Transition from hyperbolicity to ellipticity for a p-system with viscosity
In this article we consider a viscous regularization of a p-system with a Van der Waals pressure law, which presents both hyperbolic and elliptic zones. Even if the purely hyperbolic Van der Walls system is strongly ill-posed, we prove that the solutions of the regularized equation exist and expe...
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| Format: | Article |
| Language: | English |
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Texas State University
2019-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/16/abstr.html |
| Summary: | In this article we consider a viscous regularization of a p-system with
a Van der Waals pressure law, which presents both hyperbolic and elliptic
zones. Even if the purely hyperbolic Van der Walls system is strongly ill-posed,
we prove that the solutions of the regularized equation exist and experience
a transition from ellipticity to hyperbolicity, i.e. solutions issued
from initial data in the elliptic zone will enter the hyperbolic zone at
some time T>0, and viceversa. |
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| ISSN: | 1072-6691 |