×
Dias, João-Paulo; Figueira, Mário

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

J. Math. Anal. Appl. 84, 486-508 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0481.35057

Cited in 1 Review
Cited in 18 Documents

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

Keywords:

conservation laws; time decay; nonlinear Schrödinger-Hartree equations and systems; unique global solution; group of operators

Citations:

Zbl 0299.35084
PDF BibTeX XML Cite
\textit{J.-P. Dias} and \textit{M. Figueira}, J. Math. Anal. Appl. 84, 486--508 (1981; Zbl 0481.35057)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.