| Journal: | Boletim da Sociedade Paranaense de Matematica |
| Database: | PERIÓDICA |
| System number: | 000398631 |
| ISSN: | 0037-8712 |
| Authors: | Medeiros, Luis Adauto1 Limaco, Juan2 Frota, Cicero Lopes3 |
| Institutions: | 1Universidade Federal do Rio de Janeiro, Instituto de Matematica, Rio de Janeiro. Brasil 2Universidade Federal Fluminense, Instituto de Matematica e Estatistica, Niteroi, Rio de Janeiro. Brasil 3Universidade Estadual de Maringa, Departamento de Matematica, Maringa, Parana. Brasil |
| Year: | 2012 |
| Volumen: | 30 |
| Number: | 2 |
| Pages: | 19-32 |
| Country: | Brasil |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico |
| English abstract | We investigate the existence and uniqueness of weak solution for a mixed problem for wave operator of the type: L(u) = ∂ 2u ∂t2 − ∆u + |u| ρ − f, ρ > 1. The operator is defined for real functions u = u(x, t) and f = f(x, t) where (x, t) ∈ Q a bounded cylinder of Rn+1 . The nonlinearity |u| ρ brings serious difficulties to obtain global a priori estimates by using energy method. The reason is because we have not a definite sign for Z Ω |u| ρ u dx. To solve this problem we employ techniques of L. Tartar [16], see also D.H. Sattinger [12] and we succeed to prove the existence and uniqueness of global weak solution for an initial boundary value problem for the operator L(u), with restriction on the initial data u0, u1 and on the function f. With this restriction we are able to apply the compactness method and obtain the unique weak solution |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas puras, Análisis funcional, Ecuaciones diferenciales, Ecuaciones diferenciales parciales, Ecuaciones no lineales, Existencia, Unicidad, Ecuación de onda |
| Keyword: | Mathematics, Pure mathematics, Functional analysis, Differential equations, Partial differential equations, Nonlinear equations, Existence, Uniqueness, Wave equation |
| Full text: | Texto completo (Ver PDF) |
