Abstract
Nonlinear diffusion equations in one dimensional spacev t =(v m) 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 betweenv>0 andv=0. 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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Mimura, M., Nakaki, T. & Tomoeda, K. A numerical approach to interface curves for some nonlinear diffusion equations. Japan J. Appl. Math. 1, 93–139 (1984). https://doi.org/10.1007/BF03167863
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DOI: https://doi.org/10.1007/BF03167863