On a repulsion-diffusion equation with immigration
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 p...
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| Formato: | Internet publication |
| Idioma: | English |
| Publicado: |
2023
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| Summary: | 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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