Existence and asymptotic behaviour of solutions of a nonlinear evolution problem

Nelson Nery Oliveira Castro

Applications of Mathematics (1997)

  • Volume: 42, Issue: 6, page 411-420
  • ISSN: 0862-7940

Abstract

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We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for u ' ' + A u - Δ u ' + | v | ρ + 2 | u | ρ u = f 1 v ' ' + A v - Δ v ' + | u | ρ + 2 | v | ρ v = f 2 * where A is the pseudo-Laplacian operator.

How to cite

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Oliveira Castro, Nelson Nery. "Existence and asymptotic behaviour of solutions of a nonlinear evolution problem." Applications of Mathematics 42.6 (1997): 411-420. <http://eudml.org/doc/32990>.

@article{OliveiraCastro1997,
abstract = {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 *\end\{align*\} where $A$ is the pseudo-Laplacian operator.},
author = {Oliveira Castro, Nelson Nery},
journal = {Applications of Mathematics},
keywords = {nonlinear problem; existence of solutions; Galerkin method; compactness; pseudo-Laplacian; asymptotic behaviour; energy type estimates; -Laplacian; pseudo-Laplacian; Galerkin method; energy type estimates},
language = {eng},
number = {6},
pages = {411-420},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and asymptotic behaviour of solutions of a nonlinear evolution problem},
url = {http://eudml.org/doc/32990},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Oliveira Castro, Nelson Nery
TI - Existence and asymptotic behaviour of solutions of a nonlinear evolution problem
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 6
SP - 411
EP - 420
AB - 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 *\end{align*} where $A$ is the pseudo-Laplacian operator.
LA - eng
KW - nonlinear problem; existence of solutions; Galerkin method; compactness; pseudo-Laplacian; asymptotic behaviour; energy type estimates; -Laplacian; pseudo-Laplacian; Galerkin method; energy type estimates
UR - http://eudml.org/doc/32990
ER -

References

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  1. Sobre uma Equação não Linear de Vibrações. Existência de Soluções Fracas e Comportamento Assintótico, Tese de Doutorado – IMUFRJ. 
  2. 10.1007/BF01109897, Math. Zeitsch. 105 (1968), 177–195. (1968) MR0232256DOI10.1007/BF01109897
  3. Sobre um Problema de Evolução não Linear, Tese de Doutorado, IMUFRJ, 1995. (1995) 
  4. Theory of Ordinary Differential Equations, New York. 
  5. Quelques Méthodes de Résolutions des Problèmes aux Limites Non Linéaires, Dunod Paris, 1969. (1969) MR0259693
  6. 10.2969/jmsj/03040747, J. Math. Soc. Jap. (10)4 (1978), 747–762. (1978) MR0513082DOI10.2969/jmsj/03040747
  7. Weak solutions for a system of nonlinear Klein-Gordon equations, Annali Di Matemática Pura ed Applicata IV (CXLVI), 173–183. MR0916692
  8. 10.3792/pja/1195526303, Proc. Jap. Acad. 47 (1971), 950–955. (1971) Zbl0258.35017MR0312023DOI10.3792/pja/1195526303

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