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Papers Published

1. 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.