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| Publications [#8743] of Thomas P. Witelski
search www.ams.org.Papers Published
- Thomas P Witelski, An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation,
Journal of Mathematical Biology, 33, pp. 1-16, (1994)
[gz]
(last updated on 1999/11/12)
Abstract:
We examine traveling-wave solutions for a generalized
nonlinear-diffusion
Fisher equation studied by Hayes [J. Math. Biol., {\bf 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.
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