Global solutions for a supercritical drift-diffusion equation
We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/30386 |
| Acceso en línea: | https://hdl.handle.net/10902/30386 |
| Access Level: | acceso abierto |
| Palabra clave: | Drift–diffusion equation Nonlocal diffusion Global existence |
| Sumario: | We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order of the fractional diffusion α∈(1-c1, 2], where c1>0 is an explicit constant depending on the physical parameters present in the problem (chemosensitivity and strength of logistic damping). Furthermore, in the range 1-c2<α≤2 with 0<c2<c1, the solution is globally smooth. Let us emphasize that when α<1, the diffusion is in the supercritical regime. |
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