Some time-dependent Hartree equations

E. B. Davies

Annales de l'I.H.P. Physique théorique (1979)

  • Volume: 31, Issue: 4, page 319-337
  • ISSN: 0246-0211

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Davies, E. B.. "Some time-dependent Hartree equations." Annales de l'I.H.P. Physique théorique 31.4 (1979): 319-337. <http://eudml.org/doc/76051>.

@article{Davies1979,
author = {Davies, E. B.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {existence of global solutions; time-dependent Hartree equation},
language = {eng},
number = {4},
pages = {319-337},
publisher = {Gauthier-Villars},
title = {Some time-dependent Hartree equations},
url = {http://eudml.org/doc/76051},
volume = {31},
year = {1979},
}

TY - JOUR
AU - Davies, E. B.
TI - Some time-dependent Hartree equations
JO - Annales de l'I.H.P. Physique théorique
PY - 1979
PB - Gauthier-Villars
VL - 31
IS - 4
SP - 319
EP - 337
LA - eng
KW - existence of global solutions; time-dependent Hartree equation
UR - http://eudml.org/doc/76051
ER -

References

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  1. [1] A. Bove, G. Da Prato, G. Fano, On the Hartree-Fock time-dependent potential. Commun. Math. Phys., t. 49, 1976, p. 25-33. Zbl0303.34046MR456066
  2. [2] J.M. Chadam, R.T. Glassey, Global existence of solutions to the Cauchy problem for time-dependent Hertree equations. J. Math. Phys., t. 16, 1975, p. 1122-1130. Zbl0299.35084MR413843
  3. [3] E.B. Davies, Symmetry breaking for a non-linear Schrödinger equations. Commun. Math. Phys., t. 64, 1979, p. 191-216. Zbl0405.35027MR520090
  4. [4] M. Fannes, H. Spohn, A. Verbeure, Equilibrium states for mean field models. Preprint. Zbl0445.46049MR558480
  5. [5] J. Ginibre, G. Velo, The classical field limit for non-relativistic many-boson systems. I. Commun. Math. Phys., t. 66, 1979, p. 37-76. Zbl0443.35067MR530915
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  7. [7] K. Hepp, The classical limit for quantum-mechanical correlation functions. Commun. Math. Phys., t. 35, 1974, p. 265-277. MR332046
  8. [8] K. Hepp, E.H. Lieb, Phase transitions in reservoir driven open systems with applications to laser and superconductors. Helv. Phys. Acta, t. 46, 1973, p. 573-603. 
  9. [9] T. Kato, Linear evolution equations of « hyperbolic » type. J. Fac. Sci. Univ. Tokyo, Sect. 1 A, t. 17, 1970, p. 241-258. Zbl0222.47011MR279626
  10. [10] T. Kato, Quasi-linear equations of evolutions, with applications to partial differential equations. Lecture Notes in Math., t. 448, 1975, p. 25-70. Zbl0315.35077MR407477
  11. [11] E.H. Lieb, Existence and uniqueness of the minimising solutions of Choquard's non-linear equation. Stud. Appl. Math., t. 57, 1977, p. 93-106. Zbl0369.35022MR471785
  12. [12] E.H. Lieb, B. Simon, The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys., t. 53, 1977, p. 185-194. MR452286
  13. [13] E.H. Lieb, K. Yamazaki, Ground state energy and effective mass of the polaron. Phys. Rev., t. 111, 1958, p. 728-733. Zbl0100.42504
  14. [14] H. Spohn, Kinetic equations from Hamiltonian dynamics: the Markovian limit. Univ. of Leuven lecture notes, 1978/1979, Section 20. MR578142
  15. [15] E.M. Stein, Singular integrals and differentiability properties of functions. Princeton Univ. Press, 1970. Zbl0207.13501MR290095
  16. J. Ginibre, G. Velo, Équation de Schrödinger non linéaire avec interaction non locale. C. R. Acad. Sci. Paris, t. 288A, 1979, p. 683-685. Zbl0397.35013MR533902
  17. J. Ginibre, G. Velo, On a class of non-linear Schrödinger equations wi th non-local interactions. Preprint, 1979. Zbl0396.35029

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