Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
We prove existence and uniqueness of a global in time self-similar solution growing up as t → ∞ for the following reaction-diffusion equation with a singular potential ∂tu = ∆u^m + |x|^σ u^p posed in dimension N ≥ 2, with m > 1, σ ∈ (−2, 0) and 1 <p< 1 − σ (m − 1)/2. For the special case of...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/26801 |
| Acceso en línea: | https://hdl.handle.net/10115/26801 |
| Access Level: | acceso abierto |
| Palabra clave: | Reaction-diffusion equations Non-uniqueness Global solutions Singular potential Hardy-type equations Self-similar solutions. |
| Sumario: | We prove existence and uniqueness of a global in time self-similar solution growing up as t → ∞ for the following reaction-diffusion equation with a singular potential ∂tu = ∆u^m + |x|^σ u^p posed in dimension N ≥ 2, with m > 1, σ ∈ (−2, 0) and 1 <p< 1 − σ (m − 1)/2. For the special case of dimension N = 1, the same holds true for σ ∈ (−1, 0) and similar ranges for m and p. The existence of this global solution prevents finite time blow-up even with m > 1 and p > 1, showing an interesting effect induced by the singular potential |x|^σ . This result is also applied to reaction-diffusion equations with general potentials V (x) to prevent finite time blow-up via comparison. |
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