Travelling Waves in some Reaction-diffusion-aggregation Models

Ferracuti, Laura; Marcelli, Cristina; Papalini, Francesca
June 2009
Advances in Dynamical Systems & Applications;2009, Vol. 4 Issue 1, p19
Academic Journal
We deal with the reaction-diffusion-aggregation equation vt = [D(v)vx]x + f(v) t ≥ 0, x ∈ 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.


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