An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation |
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Authors: | Thomas P Witelski |
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Institution: | (1) Department of Applied Mathematics, California Institute of Technology, 217-50, 91125 Pasadena, CA, USA |
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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.
Supported by a National Science Foundation graduate fellowship. This work was performed under National Science Foundation
grant DMS-9024963 and Air Force Office of Scientific Research grant AFOSR-F49620-94-1-0044. |
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Keywords: | Fisher's equation Traveling waves Nonlinear diffusion Asymptotic expansions |
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