Parabolic equations with natural growth approximated by nonlocal equations
In this paper, we study several aspects related with solutions of nonlocal problems whose prototype is {u(t) = integral N-R J (x - y)(u(y, t) u( x, t))g (u(y , t) u( x, t))dy in Omega x (0, T), u(x, 0) = u(0)(x) in Omega, where we take, as the most important instance, g(s) similar to 1 + mu/2 s/1+mu...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/24435 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/24435 |
| Access Level: | acceso abierto |
| Palabra clave: | 12 Matemáticas nonlocal problems KPZ equation nonlinear parabolic equation sasymptotic behavior of solutions |
| Sumario: | In this paper, we study several aspects related with solutions of nonlocal problems whose prototype is {u(t) = integral N-R J (x - y)(u(y, t) u( x, t))g (u(y , t) u( x, t))dy in Omega x (0, T), u(x, 0) = u(0)(x) in Omega, where we take, as the most important instance, g(s) similar to 1 + mu/2 s/1+mu(2)s(2) with mu is an element of R as well as mu(0)is an element of L-1 (Omega), J is a smooth symmetric function with compact support and S2 is either a bounded smooth subset of R-N, with nonlocal Dirichlet boundary condition, or RN itself. The results deal with existence, uniqueness, comparison principle and asymptotic behavior. Moreover, we prove that if the kernel is resealed in a suitable way, the unique solution of the above problem converges to a solution of the deterministic Kardar Parisi Zhang equation. |
|---|