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Waiting-Time Behavior in a Nonlinear Diffusion Equation

Kath, William L. and Cohen, Donald S. (1982) Waiting-Time Behavior in a Nonlinear Diffusion Equation. Studies in Applied Mathematics, 67 (2). pp. 79-105. ISSN 0022-2526. doi:10.1002/sapm198267279.

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We study the nonlinear diffusion equation u_t*=(u^nu_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.

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Additional Information:© 1982 by the Massachusetts Institute of Technology. Manuscript received: 13 August 1981. Supported in part by the U.S. Army Research Office (Durham) under Contract DAAG29-78-C-0011 and by the National Science Foundation under Grant MCS78-03036. Supported by a National Science Foundation Graduate Fellowship.
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Army Research Office (ARO)DAAG29-78-C-0011
NSF Graduate Research FellowshipUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20200114-093322524
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Official Citation:Kath, William L., and Cohen, Donald S., (1982), Waiting‐Time Behavior in a Nonlinear Diffusion Equation, Studies in Applied Mathematics, 67, doi: 10.1002/sapm198267279.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100713
Deposited By: Tony Diaz
Deposited On:14 Jan 2020 18:07
Last Modified:16 Nov 2021 17:56

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