Critical wave speeds for a family of scalar reaction-diffusion equations

Journal article

We study the set of traveling waves in a class of reaction-diffusion equations for the family of potentials fm(U) = 2Um(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 → 2 and m → ∞. Also, an integral formulation of the problem shows that nonuniform convergence of the generalized equal area rule occurs at the critical wave speed. © 2000 Elsevier Science Ltd. All rights reserved.

Authors: Witelski, T; Ono, K; Kaper, T

• Publication status: Published
• Journal: APPLIED MATHEMATICS LETTERS
• Volume: 14
• Issue: 1
• Pages: 65-73
• Publication date: 2001-01-01
• DOI: 10.1016/S0893-9659(00)00114-2
• ISSN: 0893-9659
• Language: English
• Keywords: bi-stable potentials; reaction-diffusion; traveling waves