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.
Strani, M (Corresponding)
|Data di pubblicazione:||2019|
|Titolo:||TRANSITION FROM HYPERBOLICITY TO ELLIPTICITY FOR A p-SYSTEM WITH VISCOSITY|
|Rivista:||ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS|
|Appare nelle tipologie:||2.1 Articolo su rivista |