Eternal solutions in exponential self-similar form for a quasilinear reaction-diffusion equation with critical singular potential
We prove existence and uniqueness of self-similar solutions with exponential form u(x,t)=e^{alpha t}f(|x|e^{-beta t}), alpha, beta>0, to the quasilinear reaction-diffusion equation \partial_t u=Delta u^m+|x|^{sigma}u^p, with m>1, 1<p<m and sigma=-2(p-1)/(m-1). Such self-similar solutions...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/31917 |
| Acceso en línea: | https://hdl.handle.net/10115/31917 |
| Access Level: | acceso embargado |
| Palabra clave: | Reaction-diffusion equations weighted reaction singular potential eternal solutions exponential self-similarity global solutions |
| Sumario: | We prove existence and uniqueness of self-similar solutions with exponential form u(x,t)=e^{alpha t}f(|x|e^{-beta t}), alpha, beta>0, to the quasilinear reaction-diffusion equation \partial_t u=Delta u^m+|x|^{sigma}u^p, with m>1, 1<p<m and sigma=-2(p-1)/(m-1). Such self-similar solutions are usually known in the literature as eternal solutions since they exist for any t\in(-\infty,\infty). As an application of the existence of these eternal solutions, we show existence of global in time weak solutions with any initial condition u_0 in L^{\infty}(R^N) and, in particular, that these weak solutions remain compactly supported at any time t>0 if u_0 is compactly supported. |
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