Existence of Compactly Supported Solutions for a Degenerate Nonlinear Parabolic Equation with NonLipschitz Source Term

The aim of this paper is to prove existence of non negative compactly supported solutions for a nonlinear degenerate parabolic equation with a non Lipschitz source term in one space dimension. This equation mimics the properties of the classical $k-\epsilon$ model in the context of turbulent mixing flows with respect to nonlinearities and support properties of solutions.

To the authors' knowledge, originality of the method relies both in the fact with dealing with a non Lipschitz source term and in the comparison of not only the speed but also the acceleration of the support boundaries.

Keywords

Degenerate parabolic equation, nonLipschitz source term, k-epsilon model, speed and acceleration of support boundaries

2010 Mathematics Subject Classification

35K15, 35K65

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Published 1 January 2009