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 |
| _version_ | 1811199085592444928 |
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| author | Marta Strani |
| author_facet | Marta Strani |
| author_sort | Marta Strani |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T01:41:59Z |
| format | Article |
| id | doaj.art-b8e4c9864bd94cb3a131c723a894df6b |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T01:41:59Z |
| publishDate | 2019-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-b8e4c9864bd94cb3a131c723a894df6b2022-12-22T03:53:10ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-01-01201916,114Transition from hyperbolicity to ellipticity for a p-system with viscosityMarta Strani0 Univ. Ca Foscari, Italy 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.http://ejde.math.txstate.edu/Volumes/2019/16/abstr.htmlPhase transitionshyperbolic systemelliptic system |
| spellingShingle | Marta Strani Transition from hyperbolicity to ellipticity for a p-system with viscosity Electronic Journal of Differential Equations Phase transitions hyperbolic system elliptic system |
| title | Transition from hyperbolicity to ellipticity for a p-system with viscosity |
| title_full | Transition from hyperbolicity to ellipticity for a p-system with viscosity |
| title_fullStr | Transition from hyperbolicity to ellipticity for a p-system with viscosity |
| title_full_unstemmed | Transition from hyperbolicity to ellipticity for a p-system with viscosity |
| title_short | Transition from hyperbolicity to ellipticity for a p-system with viscosity |
| title_sort | transition from hyperbolicity to ellipticity for a p system with viscosity |
| topic | Phase transitions hyperbolic system elliptic system |
| url | http://ejde.math.txstate.edu/Volumes/2019/16/abstr.html |
| work_keys_str_mv | AT martastrani transitionfromhyperbolicitytoellipticityforapsystemwithviscosity |