Waiting-Time Behavior in a Nonlinear Diffusion Equation

William L. Kath; Donald S. Cohen

doi:10.1002/sapm198267279

Waiting-Time Behavior in a Nonlinear Diffusion Equation

William L. Kath, Donald S. Cohen^*

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

We study the nonlinear diffusion equation u_t*=(uⁿu_x)_x, which occurs in the study of a number of problems. Using singular-perturbation techniques, we construct approximate solutions of this equation in the limit of small n. These approximate solutions reveal simply the consequences of this variable diffusion coefficient, such as the finite propagation speed of interfaces and waiting-time behavior (when interfaces wait a finite time before beginning to move), and allow us to extend previous results for this equation.

Original language	English (US)
Pages (from-to)	79-105
Number of pages	27
Journal	Studies in Applied Mathematics
Volume	67
Issue number	2
DOIs	https://doi.org/10.1002/sapm198267279
State	Published - Oct 1 1982

ASJC Scopus subject areas

Applied Mathematics

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Waiting-Time Behavior in a Nonlinear Diffusion Equation

Abstract

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