Pushed Travelling Waves in an Initial-Boundary Value Problem for Fisher Type Equations

摘要

The initial boundary value problem for the semilinear diffusion equation u sub(t) equals u sub(xx) + f(u) on the half-line x 0 is considered for f(0) equals f(1) equals 0 and f(u) 0 when 0 u 1. This equation can serve as a model for the spread of an allele (A) in a diploid population with zygotes AA Aa and aa. A uniformly valid asymptotic expression with exponentially converging solutions is given for a wide class of initial and boundary values. This expression is composed of a travelling wave with a minimum velocity c(f) 2 square root of f prime (0) and a solution to the stationary problem.