Travelling Waves in some Reaction-diffusion-aggregation Models

Abstract

We deal with the reaction-diffusion-aggregation equation vt = h D(v)vx i x + f(v) t 0, x 2 R, where f is a monostable (i.e., Fisher-type) nonlinear reaction term and D(v) is a changing-sign nonlinear term, modeling repulsive-attractive population dynamic. We prove the existence of travelling fronts having speed varying in a half-line and provide an estimate for the minimal speed c . We also investigate the possible existence of fronts reaching the equilibria at finite values.