Strani, Marta2021-10-152021-10-152019-01-28Strani, M. (2019). Transition from hyperbolicity to ellipticity for a p-system with viscosity. <i>Electronic Journal of Differential Equations, 2019</i>(16), pp. 1-14.1072-6691https://hdl.handle.net/10877/14659In 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.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalPhase transitionsHyperbolic systemElliptic systemArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.