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

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 → 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.