The spreading property for a prey-predator reaction-diffusion system with fractional diffusion
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AbstractThis paper is devoted to the study of some spreading properties of a prey-predator reaction-diffusion system where the diffusion term is replaced by the fractional Laplacian. We focus on the invasion of the introduced predator in some environment which is initially well-populated of prey. In contrast with the case of the standard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable Lévy process, the front position is exponential in time.
1998 ◽
Vol 63
(6)
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pp. 761-769
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2021 ◽
Vol 31
(3)
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pp. 033118
1985 ◽
Vol 114
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pp. 243-272
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2002 ◽
Vol 161
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pp. 45-66
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