When fast diffusion and reactive growth both induce accelerating invasions

Matthieu Alfaro (1) , Thomas Giletti (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 IECL - Institut Élie Cartan de Lorraine

We focus on the spreading properties of solutions of monostable equations with fast diffusion. The nonlinear reaction term involves a weak Allee effect, which tends to slow down the propagation. We complete the picture of [3] by studying the subtle case where acceleration does occur and is induced by a combination of fast diffusion and of reactive growth. This requires the construction of new elaborate sub and supersolutions thanks to some underlying self-similar solutions.

Mots clés: reaction-diffusion equations; spreading properties; fast diffusion; self-similar solutions; acceleration

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Alfaro, Thomas Giletti. When fast diffusion and reactive growth both induce accelerating invasions. Communications on Pure and Applied Analysis, 2019, 18 (6), pp.3011-3034. ⟨10.3934/cpaa.2019135⟩. ⟨hal-01874703v2⟩