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| Many biological and ecological phenomena occur in which organisms or diseases diffuse faster in some parts of the environment, typically along roads or rivers. Recently, H. Berestycki, J.-M. Roquejoffre and L. Rossi have introduced a new PDE model to study the effect on the asymptotic speed of propagation of such diffusion heterogeneity produced by a line which bounds a half plane where a classical logistic reproduction of Fisher-KPP type takes place. The novelty consists in the fact that the equations are posed in different spatial dimensions. In this talk we will analyze the effect that two roads with different diffusion have on the propagation in a strip bounded by them. We will study the limits as the diffusion on the roads goes to $0$ and $\infty$ and the limit as the width of the strip goes to $0$ and $\infty$. In the latter case we recover the asymptotic speed of propagation of the half plane. This is a joint work with L. Rossi (Univ. Padova, Italy) and E. Valdinoci (WIAS, Berlin). |
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