An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation

✍ Scribed by Thomas P. Witelski

• Publisher: Springer
• Year: 1994
• Tongue: English
• Weight: 734 KB
• Volume: 33
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00160171

✦ Synopsis

We examine traveling-wave solutions for a generalized nonlineardiffusion 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.