Nonlocal heat equations in the Heisenberg group
We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that the asymptotic behavior of the solutions is the same form that the one for the...
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/59992 |
| Acesso em linha: | http://hdl.handle.net/11336/59992 |
| Access Level: | acceso abierto |
| Palavra-chave: | HEISENBERG GROUP NONLOCAL DIFFUSION SPHERICAL TRANSFORM https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that the asymptotic behavior of the solutions is the same form that the one for the parabolic equation for the fractional laplace operator. To obtain this result we use the spherical transform related to the pair (U(n) , Hn). Finally we prove that solutions of properly rescaled nonlocal Dirichlet problem converge uniformly to the solution of the corresponding Dirichlet problem for the classical heat equation in the Heisenberg group. |
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