Travelling Waves in someReaction-diffusion-aggregation Models

摘要

We deal with the reaction-diffusion-aggregation equation v_t=[D(v)v_x]+f(v)t≥0,x∈R, where f is a monostable (i.e., Fisher-type) nonlinear reaction term and D(v) is achanging-sign nonlinear term, modeling repulsive-attractive population dynamic.We prove the existence of travelling fronts having speed varying in a half-line andprovide an estimate for the minimal speed c~*.We also investigate the possibleexistence of fronts reaching the equilibria at finite values.