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.

TRANSITION FROM HYPERBOLICITY TO ELLIPTICITY FOR A p-SYSTEM WITH VISCOSITY

Strani, M
2019

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10278/3716930
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