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- W2079210236 abstract "We study the propagation of a front arising as theasymptotic (macroscopic) limit of a model in spatial ecologyin which the invasive species propagate by 'jumps'. The evolution of the orderparameter marking the location of the colonized/uncolonized sites is governedby a (mesoscopic) integro-differential equation. Thisequation has structure similar to the classical Fisher or KPP - equation,i.e., it admits two equilibria, a stable one at $k$ and an unstable one at $0$describing respectivelythe colonized and uncolonized sites. We prove that,after rescaling, the solution exhibits a sharp frontseparating the colonized anduncolonized regions, and we identify its (normal) velocity. In somespecial cases the front follows a geometric motion. We also consider thesame problem in heterogeneous habitats and oscillating habitats. Our methods, whichare based on theanalysis of a Hamilton-Jacobi equation obtained after a change ofvariables, follow arguments which were already used in thestudy of the analogous phenomena for the Fisher/KPP - equation." @default.
- W2079210236 created "2016-06-24" @default.
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- W2079210236 date "2005-01-01" @default.
- W2079210236 modified "2023-09-24" @default.
- W2079210236 title "Front propagation for a jump process model arising in spacial ecology" @default.
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- W2079210236 doi "https://doi.org/10.3934/dcds.2005.13.1235" @default.
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