Propagation Phenomena with Nonlocal Diffusion in Presence of an Obstacle

نویسندگان

چکیده

We consider a nonlocal semi-linear parabolic equation on connected exterior domain of the form $${\mathbb {R}}^N\setminus K$$ , where $$K\subset {\mathbb {R}}^N$$ is compact “obstacle”. The model we study motivated by applications in biology and takes into account long range dispersal events that may be anisotropic depending how given population perceives environment. To formulate this meaningful manner, introduce new theoretical framework which both mathematical biological interest. main goal paper to construct an entire solution behaves like planar travelling wave as $$t\rightarrow -\infty $$ propagates shape obstacle. show whether recovers front large time limit equivalent certain Liouville type property satisfied. validity extend some previous results Hamel, Valdinoci authors. Lastly, generalised transition front.

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ژورنال

عنوان ژورنال: Journal of Dynamics and Differential Equations

سال: 2021

ISSN: ['1040-7294', '1572-9222']

DOI: https://doi.org/10.1007/s10884-021-09988-y