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arXiv · 2304.06990

On a Repulsion-Diffusion Equation with Immigration

Peter Koepernik
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Abstract

We study a repulsion-diffusion equation with immigration, whose asymptotic behaviour is related to stability of long-term dynamics in spatial population models and other branching particle systems. We prove well-posedness and find sharp conditions on the repulsion under which a form of the maximum principle and a strong notion of global boundedness of solutions hold. The critical asymptotic strength of the repulsion is $|x|^{1-d}$, that of the Newtonian potential.

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Peter Koepernik. 2023-04-14. On a Repulsion-Diffusion Equation with Immigration. https://arxiv.org/abs/2304.06990

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