Global existence and uniform decay for the coupled Klein-Gordon-Schrödinger equations

Nonlinear Differential Equations and Applications

Volumn 7, Issue 3, 2000, Pages 285-307

  Cavalcanti, M M ^a   Cavalcanti, V N Domingos ^a  

^a STATE UNIVERSITY OF MARINGÁ   (Brazil)

Author keywords

Energy methods; Galerkin approximation; Klein gordon schr dinger equations

Indexed keywords

EID: 0348246754     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001426     Document Type: Article

References (12)

1. A. BACHELOT, Problème de Cauchy pour des systèmes hyperboliques semilinéares, Ann. Inst. H. Poincaré Anal, non Linéaire 1 (1984), pp. 453-478.
2. J.B. BAILLON, J.M. CHADAM, The Cauchy problem for the coupled Klein-Gordon-Schrödinger equations, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations, North Holland, Amsterdam, (1978), pp. 37-44.
3. I. FUKUDA, M. TSUTSUMI, On coupled Klein-Gordon-Schrödinger equations I, Bull. Sci. Engrg. Res. Lab. Waseda Univ. 69 (1975), pp. 51-62.
4. I. FUKUDA, M. TSUTSUMI, On coupled Klein-Gordon-Schrödinger equations II, J. Math. Analysis Applic. 66 (1978), pp. 358-378.
5. I. FUKUDA, M. TSUTSUMI, On coupled Klein-Gordon-Schrödinger equations III - Higher order interaction, decay and blow-up, Math. Japonica 24 (1979), pp. 307-321.
6. I. FUKUDA, M. TSUTSUMI, On the Yukawa-coupled Klein-Gordon-Schrödinger equations in three space dimensions, Proc. Japan Acad. 51 (1975), pp. 402-405.
7. A. HARAUX, E. ZUAZUA, Decay estimates for some semilinear damped hyperbolic problems, Archives for Rational Mechanics and Analysis, 100 (2) (1988), pp. 191-206.
8. N. HAYASHI, W. VON WAHL, On the global strong solutions of coupled Klein-Gordon-Schrödinger equations, J. Math. Soc. Japan 39 (1987), pp. 489-497.
9. J.L. LIONS, Quelques Métodes de Résolution des Problèmes Aux Limites Non Linéaires, Dunod, Paris, 1969.
10. J.L. LIONS, E. MAGENES, Problèmes Aux Limites non Homogènes et Applications, Dunod, Paris, 1968, Vol. 1.
11. M. OHTA, Stability of Stationary States for the Coupled Klein-Gordon-Schrödinger Equations, Nonlinear Analysis, Theory, Methods and Appl. 27 (4) (1996), pp. 455-461.
12. H. YUKAWA, On the interaction of elementary particles I, Proc. Physico-Math. Soc. Japan 17 (1935), pp. 48-57.