Travelling Wave Solutions of a Nonlinear Diffusion Equation with Integral Term

Abstract

Travelling wave solutions with compact support are investigated for a class of nonlinear nonlocal degenerate diffusion equations introduced by T. Nagai and M. Mimura. The problem is reduced to a boundary value problem for an integro-differential equation of second order and in turn to an integral equation with nonnegative kernel. There are given existene proofs for three types of power nonlinearities in case of a general integral term and closed solutions for a simple integral term.