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

✍ Scribed by T.P. Witelski; K. Ono; T.J. Kaper

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 481 KB
• Volume: 14
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(00)00114-2

✦ Synopsis

We study the set of traveling waves in a class of reaction-diffusion equations for the family of potentials fro(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 ---* 2 and m --~ oe. Also, an integral formulation of the problem shows that nonuniform convergence of the generalized equal area rule occurs at the critical wave speed.