Math @ Duke

Publications [#9523] of Thomas P. Witelski
search www.ams.org.Papers Accepted
 Thomas P. Witelski, K. Ono, T. J. Kaper, Analysis of the critical wave speeds of scalar reactiondiffusion equations,
Applied Math Letters, [Boston University Center for BioDynamics Technical Report No. 5, (1998)]
, accepted 2000 [ps]
(last updated on 2000/01/24)
Abstract: We study the set of traveling waves in a class of
reactiondiffusion
equations for the family of potentials $f_m(U)=2U^m(1U)$.
We use perturbation methods and matched asymptotics to
derive
expansions for the critical wave speed that separates
algebraic and
exponential traveling wave front solutions for $m\to 2$ and
$m\to\infty$. Also, an integral formulation of the problem
shows that
nonuniform convergence
of the generalized equal area rule occurs at the critical
wave speed.


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