Blocking and invasion for reaction-diffusion equations in periodic media

Romain Ducasse (1) , Luca Rossi (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

We investigate the large time behavior of solutions of reaction-diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade the domain. In particular, we relate such solutions with front-like solutions such as pulsating traveling fronts. Next, we focus on the homogeneous equation set in a domain with periodic holes, and specifically in the cases where fronts are not known to exist. We show how the geometry of the domain can block or allow invasion. We finally exhibit a periodic domain on which the propagation takes place in an asymmetric fashion, in the sense that the invasion occurs in a direction but is blocked in the opposite one.

Mots clés: invasion; spreading; domains with holes; reaction-diffusion equations; propagation

Domaines: Equations aux dérivées partielles [math.AP]

Romain Ducasse, Luca Rossi. Blocking and invasion for reaction-diffusion equations in periodic media. Calculus of Variations and Partial Differential Equations, 2018, 57 (5), ⟨10.1007/s00526-018-1412-0⟩. ⟨hal-01637967v2⟩