Publications [#244190] of Thomas P. Witelski

Papers Published

1. Witelski, TP, An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation, Journal of Mathematical Biology, vol. 33 no. 1 (November, 1994), pp. 1-16, Springer Nature, ISSN 0303-6812 [gz], [doi]
   (last updated on 2024/04/18)

   Abstract:
   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.