Nonlinear diffusion equations in one dimensional space vt=(vm)xx+vF(v) (m> 1) appear in the fields of fluid dynamics, combustion theory, plasma physics and population dynamics. The most interesting phenomenon is the finite speed of propagation. Specifically, if the initial function has compact support, the solution has also compact support for later times, and there appears an interface between v >0 and v=O. The aim of this paper is to propose a finite difference scheme possessing the property that numerical solutions as well as numerical interfaces converge to the exact ones. Numerical examples are also presented.

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Abstract.We consider the nonlinear degenerate diffusion equation. The most striking manifestation of the nonlinearity and degeneracy is an appearance of interfaces. Under some condition imposed on the initial function, the interfaces do not move on some time interval [0, t*]. In this paper, from numerical points of view, we try to determine the value of t*, which is called the waiting time.

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