Transition from hyperbolicity to ellipticity for a p-system with viscosity
Date
2019-01-28
Authors
Strani, Marta
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Phase transitions, Hyperbolic system, Elliptic system
Citation
Strani, M. (2019). Transition from hyperbolicity to ellipticity for a p-system with viscosity. <i>Electronic Journal of Differential Equations, 2019</i>(16), pp. 1-14.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.