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September  2008, 22(3): 729-758. doi: 10.3934/dcds.2008.22.729

On a class of equations with variable parabolicity direction

Flavia Smarrazzo 1,

1. 

Department of Mathematics “G. Castelnuovo”, University of Rome “La Sapienza”, P.le A. Moro 5, I-00185 Roma, Italy

Received  July 2007 Revised  February 2008 Published  August 2008

We consider the following pseudoparabolic regularization of a forward-backward quasilinear diffusion equation: $u_t=\Delta \phi(u)+\varepsilon\Delta u_t$ ($\varepsilon>0$). As suggested by several models of the applied sciences, the function $\phi$ is nonmonotone and vanishing at infinity. We investigate the limit points of the set of solutions to the associated Neumann problem as $\varepsilon\to 0$, proving existence of suitable weak solutions of the original ill-posed equation. Qualitative properties of such solutions are also addressed.
Keywords: Forward-backward parabolic equations, pseudoparabolic regularization, Young measures..
Mathematics Subject Classification: Primary: 35K20, 35K55; Secondary: 28A33, 28A5.
Citation: Flavia Smarrazzo. On a class of equations with variable parabolicity direction. Discrete & Continuous Dynamical Systems, 2008, 22 (3) : 729-758. doi: 10.3934/dcds.2008.22.729
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