Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
We deal with radially symmetric solutions to the reaction-diffusion equation with Hardy-type singular potential ut = Δum + K |x|2 um, posed in RN × (0, T), in dimension N ≥ 3, where m > 1 and 0 <K< (N − 2)2/4. We prove that, in dependence of the initial condition u0 ∈ L∞(RN ) ∩ C(RN ), its...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/29823 |
| Acceso en línea: | https://hdl.handle.net/10115/29823 |
| Access Level: | acceso abierto |
| Palabra clave: | Reaction-diffusion equations Hardy-type potential Instantaneous blow-up Non-homogeneous porous medium |
| Sumario: | We deal with radially symmetric solutions to the reaction-diffusion equation with Hardy-type singular potential ut = Δum + K |x|2 um, posed in RN × (0, T), in dimension N ≥ 3, where m > 1 and 0 <K< (N − 2)2/4. We prove that, in dependence of the initial condition u0 ∈ L∞(RN ) ∩ C(RN ), its solutions may either blow up instantaneously or blow up in finite time at the origin, thus developing a singularity at x = 0, but they can be continued globally in weak sense. The instantaneous blow-up occurs for example for any data u0 such that u0(0) > 0. The proofs are based on a transformation mapping solutions to our equation into solutions to a non-homogeneous porous medium equation. |
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