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Conservation laws and time decay for the solutions of some nonlinear Schrödinger-Hartree equations and systems. (English) Zbl 0481.35057

MSC:
35L65 Hyperbolic conservation laws
35G25 Initial value problems for nonlinear higher-order PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
35Q99 Partial differential equations of mathematical physics and other areas of application
35B40 Asymptotic behavior of solutions to PDEs
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References:
[1] Bers, L; John, F; Schechter, M, Partial differential equations, (1964), Interscience New York
[2] Chadam, J.M; Glassey, R.T, Global existence of solutions to the Cauchy problem for time-dependent Hartree equations, J. math. phys., 16, 112-1130, (1975) · Zbl 0299.35084
[3] Dias, J.P; Figueira, M, Décroissance à l’infini de la solution d’une équation non linéaire du type Schrödinger-Hartree, C. R. acad. sci. Paris Sér. A, 290, 889-892, (1980) · Zbl 0442.35013
[4] Ginibre, J; Velo, G, On a class of nonlinear Schrödinger equations. II. scattering theory, general case, J. funct. anal., 32, 33-71, (1979) · Zbl 0396.35029
[5] Ginibre, J; Velo, G, Équation de Schrödinger non linéaire avec interaction non locale, C. R. acad. sci. Paris Sér. A, 288, 683-685, (1979) · Zbl 0397.35013
[6] Glassey, R.T, Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations, Comm. math. phys., 53, 9-18, (1977) · Zbl 0339.35013
[7] Lions, J.L, Quelques méthodes de résolution des problèmes aux limites non linéaires, (1969), Dunod/Gauthier-Villars Paris · Zbl 0189.40603
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