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A singular limit in a fractional reaction-diffusion equation with periodic coefficients. (English) Zbl 1417.35069
Summary: We provide an asymptotic analysis of a non-local Fisher-KPP-type equation in periodic media and with a non-local stable operator of order $$\alpha \in (0,1)$$. We perform a long time-long range scaling in order to prove that the stable state invades the unstable state with a speed which is exponential in time.

MSC:
 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs 35Q92 PDEs in connection with biology, chemistry and other natural sciences
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