An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation
Published
Journal Article
We examine traveling-wave solutions for a generalized nonlinear-diffusion Fisher equation studied by Hayes [J. Math. Biol. 29, 531-537 (1991)]. The density-dependent diffusion coefficient used is motivated by certain polymer diffusion and population dispersal problems. Approximate solutions are constructed using asymptotic expansions. We find that the solution will have a corner layer (a shock in the derivative) as the diffusion coefficient approaches a step function. The corner layer at z = 0 is matched to an outer solution for z < 0 and a boundary layer for z > 0 to produce a complete solution. We show that this model also admits a new class of nonphysical solutions and obtain conditions that restrict the set of valid traveling-wave solutions. © 1994 Springer-Verlag.
Full Text
Duke Authors
Cited Authors
- Witelski, TP
Published Date
- November 1, 1994
Published In
Volume / Issue
- 33 / 1
Start / End Page
- 1 - 16
Electronic International Standard Serial Number (EISSN)
- 1432-1416
International Standard Serial Number (ISSN)
- 0303-6812
Digital Object Identifier (DOI)
- 10.1007/BF00160171
Citation Source
- Scopus