| Texto completo | |
| Autor(es): |
Bezerra, F. D. M.
;
Nascimento, M. J. D.
;
da Silva, S. H.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | APPLICABLE ANALYSIS; v. 96, n. 13, p. 2180-2191, 2017. |
| Citações Web of Science: | 2 |
| Resumo | |
In this paper we consider the following nonlinear and spatially nonlocal second-order evolution equation from nonlocal theory of continuum mechanics [u(tt) + a(t, x) u(t) - integral(RN) J(x, y)(beta u(y) - u(x)) dy = f (u), x is an element of Omega, t > tau, u(x, tau) = u(0)(x), u(tau) (x, tau) = u(1)(x), x is an element of Omega, u(x, t) = 0, x is an element of R-n\textbackslash{}Omega, t >= tau, where Omega is a bounded smooth domain in R-n, n >= 3, 0 < beta < 1, and a is a bounded continuous function. Here, the kernel J is a nonnegative, symmetric bounded function with bounded derivative, satisfying certain growth conditions. We deduce an energy functional associated to these problem, and we study the local and global well posedness, boundedness and asymptotic behavior of its solutions. Additionally we study the stability of the trivial solution associated to these problem. (AU) | |
| Processo FAPESP: | 14/03686-3 - A dinâmica de equações de evolução governadas por potências fracionárias de operadores fechados |
| Beneficiário: | Flank David Morais Bezerra |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 14/03109-6 - Dinâmica de problemas semilineares autônomos e não-autônomos |
| Beneficiário: | Marcelo José Dias Nascimento |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |