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On a coupled set of nonlinear diffusion equations

Authors :
Stevens F. Johnson
Karl E. Lonngren
Source :
Journal of Applied Physics. 51:5201
Publication Year :
1980
Publisher :
AIP Publishing, 1980.

Abstract

We show that the set of coupled nonlinear diffusion equations nt =μnxx−d [(n/s)sx]x and st =Dsxx−AnsB admits a self‐similar solution. These equations have been used in biology to model the migration of bacteria into a substrate. An asymptotic solution in the limit of large η≡x/(4xt)1/2 is obtained.

Details

ISSN :
00218979
Volume :
51
Database :
OpenAIRE
Journal :
Journal of Applied Physics
Accession number :
edsair.doi...........033ed99c50cb478b6be7602cbd3bc784
Full Text :
https://doi.org/10.1063/1.327433