- Thomas P. Witelski, K. Ono, T. J. Kaper, Analysis of the critical wave speeds of scalar reaction-diffusion equations,
Applied Math Letters, 14/1 (2000) pp. 65-73.
(last updated on 2000/10/16)
We study the set of traveling waves in a class of reaction-diffusion equations for the family of potentials $f_m(U)=2U^m(1-U)$. 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.