Propagation phenomena for time heterogeneous KPP reaction–diffusion equationsReport as inadecuate




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1 LJLL - Laboratoire Jacques-Louis Lions 2 Dipartimento di Matematica padova

Abstract : We investigate in this paper propagation phenomena for the heterogeneous reaction-diffusion equation ∂ t u − ∆u = f t, u, x ∈ R N , t ∈ R, where f = f t, u is a KPP monostable nonlinearity which depends in a general way on t ∈ R. A typical f which satisfies our hypotheses is f t, u = µtu1 − u, with µ ∈ L ∞ R such that ess inf t∈R µt > 0. We first prove the existence of generalized transition waves recently defined in 4, 22 for a given class of speeds. As an appli-cation of this result, we obtain the existence of random transition waves when f is a random stationary ergodic function with respect to t ∈ R. Lastly, we prove some spreading properties for the solution of the Cauchy problem.

Keywords : generalized transition waves heterogeneous reaction-diffusion equations spreading properties





Author: Grégoire Nadin - Luca Rossi -

Source: https://hal.archives-ouvertes.fr/



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