Math @ Duke

Publications [#244193] of Thomas P. Witelski
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 Witelski, TP, Merging traveling waves for the porousFisher's equation,
Applied Mathematics Letters, vol. 8 no. 4
(1995),
pp. 5762, ISSN 08939659
(last updated on 2018/03/21)
Abstract: We study a reactiondiffusion equation model for population dynamics. By focusing on the diffusive behavior expected in a population that seeks to avoid overcrowding, we derive a nonlineardiffusion porousFisher's equation. Using explicit traveling wave solutions, initiallyseparated, expanding populations are studied as they first coalesce. The nonlinear interactions of the merging populations are examined using perturbation theory and the method of matched asymptotic expansions. Results are also extended to the axisymmetric case. © 1995.


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