Math @ Duke

Publications [#244190] of Thomas P. Witelski
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 Witelski, TP, An asymptotic solution for traveling waves of a nonlineardiffusion Fisher's equation,
Journal of Mathematical Biology, vol. 33 no. 1
(1994),
pp. 116, ISSN 03036812 [gz], [doi]
(last updated on 2018/10/18)
Abstract: We examine travelingwave solutions for a generalized nonlineardiffusion Fisher equation studied by Hayes [J. Math. Biol. 29, 531537 (1991)]. The densitydependent 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 travelingwave solutions. © 1994 SpringerVerlag.


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