| Title:
|
Existence and asymptotic behaviour of solutions of a nonlinear evolution problem (English) |
| Author:
|
de Oliveira Castro, Nelson Nery |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
42 |
| Issue:
|
6 |
| Year:
|
1997 |
| Pages:
|
411-420 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for \begin{align*} &u^{\prime\prime} + Au - \Delta u^\prime + |v|^{\rho +2}\,|u|^\rho \,u = f_1\\ &v^{\prime\prime} + Av - \Delta v^\prime + |u|^{\rho +2}\,|v|^\rho \,v = f_2 \tag{*}\end{align*} where $A$ is the pseudo-Laplacian operator. (English) |
| Keyword:
|
nonlinear problem |
| Keyword:
|
existence of solutions |
| Keyword:
|
Galerkin method |
| Keyword:
|
compactness |
| Keyword:
|
pseudo-Laplacian |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
energy type estimates |
| MSC:
|
34G20 |
| MSC:
|
35A05 |
| MSC:
|
35B40 |
| MSC:
|
35L55 |
| MSC:
|
35L70 |
| idZBL:
|
Zbl 0940.35139 |
| idMR:
|
MR1475050 |
| DOI:
|
10.1023/A:1022251012703 |
| . |
| Date available:
|
2009-09-22T17:55:59Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134367 |
| . |
| Reference:
|
[1] A. Biazutti: Sobre uma Equação não Linear de Vibrações. Existência de Soluções Fracas e Comportamento Assintótico.Tese de Doutorado – IMUFRJ. |
| Reference:
|
[2] F.E. Browder, Bui An Ton.: Nonlinear functional equations in Banach spaces and elliptic super regularization.Math. Zeitsch. 105 (1968), 177–195. MR 0232256, 10.1007/BF01109897 |
| Reference:
|
[3] N.N. Castro: Sobre um Problema de Evolução não Linear.Tese de Doutorado, IMUFRJ, 1995. |
| Reference:
|
[4] E. Coddington, N. Levinson: Theory of Ordinary Differential Equations.New York. |
| Reference:
|
[5] J.L. Lions: Quelques Méthodes de Résolutions des Problèmes aux Limites Non Linéaires.Dunod Paris, 1969. MR 0259693 |
| Reference:
|
[6] M. Nakao: A difference inequality and its applications to nonlinear evolution equations.J. Math. Soc. Jap. (10)4 (1978), 747–762. MR 0513082, 10.2969/jmsj/03040747 |
| Reference:
|
[7] L.A. Medeiros, M.M. Miranda: Weak solutions for a system of nonlinear Klein-Gordon equations.Annali Di Matemática Pura ed Applicata IV (CXLVI), 173–183. MR 0916692 |
| Reference:
|
[8] M. Tsutsumi: Some nonlinear evolution equations of second order.Proc. Jap. Acad. 47 (1971), 950–955. Zbl 0258.35017, MR 0312023, 10.3792/pja/1195526303 |
| . |
