Transition from hyperbolicity to ellipticity for a p-system with viscosity
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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.
CitationStrani, M. (2019). Transition from hyperbolicity to ellipticity for a p-system with viscosity. Electronic Journal of Differential Equations, 2019(16), pp. 1-14.
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