Electron. J. Differential Equations, Vol. 2019 (2019), No. 16, pp. 1-14.

Transition from hyperbolicity to ellipticity for a p-system with viscosity

Marta Strani

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.

Submitted December 12, 2018. Published January 28, 2019.
Math Subject Classifications: 35B36, 35L45, 35Q31, 76N10.
Key Words: Phase transitions; hyperbolic system; elliptic system.

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Marta Strani
Università Ca' Foscari
Dipartimento di Scienze Molecolari e Nanosistemi (DSMN)
Via Torino 155, Venezia Mestre, 30172 Italy
email: marta.strani@unive.it

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