Solutions self-similaires de l'équation de Schrödinger non-linéaire

Thierry Cazenave

Journées équations aux dérivées partielles (1997)

  • page 1-17
  • ISSN: 0752-0360

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Cazenave, Thierry. "Solutions self-similaires de l'équation de Schrödinger non-linéaire." Journées équations aux dérivées partielles (1997): 1-17. <http://eudml.org/doc/93344>.

@article{Cazenave1997,
author = {Cazenave, Thierry},
journal = {Journées équations aux dérivées partielles},
keywords = {existence; selfsimilar solutions; global solutions},
language = {fre},
pages = {1-17},
publisher = {Ecole polytechnique},
title = {Solutions self-similaires de l'équation de Schrödinger non-linéaire},
url = {http://eudml.org/doc/93344},
year = {1997},
}

TY - JOUR
AU - Cazenave, Thierry
TI - Solutions self-similaires de l'équation de Schrödinger non-linéaire
JO - Journées équations aux dérivées partielles
PY - 1997
PB - Ecole polytechnique
SP - 1
EP - 17
LA - fre
KW - existence; selfsimilar solutions; global solutions
UR - http://eudml.org/doc/93344
ER -

References

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  1. [1] M. Cannone, A generalization of a theorem by Kato on Navier-Stokes equations, preprint. Zbl0897.35061
  2. [2] M. Cannone and F. Planchon, Self-similar solutions for the Navier-Stokes equations in ℝ3, Comm. Partial Differential Equations 21 (1996), 179-193. Zbl0842.35075MR97a:35172
  3. [3] T. Cazenave and F. B. Weissler, The Cauchy problem for the critical nonlinear Schrödinger equation in Hs, Nonlinear Anal. T.M.A. 14 (1990), 807-836. Zbl0706.35127MR91j:35252
  4. [4] T. Cazenave and F. B. Weissler, The structure of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation, Proc. Royal Soc. Edinburgh Sect. A 117 (1991), 251-273. Zbl0733.35094MR92c:35111
  5. [5] T. Cazenave and F. B. Weissler, Rapidly decaying solutions of the nonlinear Schrödinger equation, Comm. Math. Phys. 147 (1992), 75-100. Zbl0763.35085MR93d:35150
  6. [6] T. Cazenave and F. B. Weissler, Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z., to appear. Zbl0916.35109
  7. [7] T. Cazenave and F. B. Weissler, More self-similar solutions of the nonlinear Schrödinger equation, to appear. Zbl0990.35121
  8. [8] M. Escobedo and O. Kavian, Asymptotic behavior of positive solutions of a nonlinear heat equation, Houston J. Math. 13 (1987), 39-50. Zbl0666.35046
  9. [9] M. Escobedo and O. Kavian, Variational problems related to self-similar solutions of the heat equation, Nonlinear Anal. 11 (1987), 1103-1133. Zbl0639.35038MR90a:35128
  10. [10] M. Escobedo, O. Kavian and H. Matano, Large time behavior of solutions of a dissipative semi-linear heat equation, Comm. Partial Differential Equations 20 (1995), 1427-1452. Zbl0838.35015MR96f:35074
  11. [11] H. Fujita, On the blowing-up of solutions of the Cauchy problem for ut = Δu + uα+1, J. Fac. Sci. Univ. Tokyo 13 (1966), 109-124. Zbl0163.34002MR35 #5761
  12. [12] H. Fujita, On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math. 18, Amer. Math. Soc., 1968, 138-161. 
  13. [13] H. Fujita and T. Kato, On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16 (1964), 269-315. Zbl0126.42301MR29 #3774
  14. [14] Y. Giga, Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system, J. Diff. Eq. 62 (1986), 186-212. Zbl0577.35058MR87h:35157
  15. [15] Y. Giga and R.V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 38 (1985), 297-319. Zbl0585.35051MR86k:35065
  16. [16] Y. Giga and R.V. Kohn, Characterizing blow up using similarity variables, Indiana Math. J. 36 (1987), 1-40. Zbl0601.35052MR88c:35021
  17. [17] Y. Giga and R.V. Kohn, Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math. 62 (1989), 845-885. Zbl0703.35020MR90k:35034
  18. [18] Y. Giga and T. Miyakawa, Solutions in Lr of the Navier-Stokes initial value problem, Arch. Rat. Mech. Anal. 89 (1985), 267-281. Zbl0587.35078MR86m:35138
  19. [19] Y. Giga and T. Miyakawa, Navier-Stokes flow in ℝ3 with measures as initial vorticity and Morrey spaces, Commun. Partial Differential Equations 14 (1989), 577-618. Zbl0681.35072MR90e:35130
  20. [20] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations I, II, J. Func. Anal. 32 (1979), 1-71. Zbl0396.35028MR82c:35057
  21. [21] A. Haraux and F.B. Weissler, Non uniqueness for a semilinear initial value problem, Indiana Univ. Math. J. 31 (1982), 167-189. Zbl0465.35049MR83h:35063
  22. [22] M.A. Herrero and J.J.L. Velázquez, Blow-up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poincaré, Analyse Non-Linéaire 10 (1993), 131-189. Zbl0813.35007MR94g:35030
  23. [23] M.A. Herrero and J.J.L. Velázquez, Some results on blow up for some semilinear parabolic problems, in Degenerate diffusion (Minneapolis, 1991), IMA Vol. Math. Appl. 47, Springer, New York, 1993, 105-125. Zbl0828.35056MR95b:35030
  24. [24] R. Johnson and X. Pan, On an elliptic equation related to the blow-up phenomenon in the non-linear Schrödinger equation, Proc. Royal Soc. Edin. Sect. A 123 (1993), 763-782. Zbl0788.35041MR94e:35059
  25. [25] T. Kato, Strong Lp solutions of the Navier-Stokes equation in ℝm, with applications to weak solutions, Math. Z. 187 (1984), 471-480. Zbl0545.35073MR86b:35171
  26. [26] T. Kato, Nonlinear Schrödinger equations, in Schrödinger Operators, Lecture Notes in Physics 345, Springer, 1989, 218-263. Zbl0698.35131MR91d:35202
  27. [27] T. Kato and H. Fujita, On the nonstationary Navier-Stokes system, Rend. Sem. Mat. Univ. Padova 32 (1962), 243-260. Zbl0114.05002MR26 #495
  28. [28] O. Kavian, Remarks on the time behaviour of a nonlinear diffusion equation, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 4 (1987), 423-452. Zbl0653.35036MR89b:35013
  29. [29] O. Kavian and F. B. Weissler, Self-similar solutions of the pseudo-conformally invariant nonlinear Schrödinger equation, Mich. Math. J. 41 (1992), 151-173. Zbl0809.35125MR95d:35165
  30. [30] N. Kopell and M. Landman, Spatial structure of the focusing singularity of the nonlinear Schrödinger equation: a geometric analysis, SIAM J. Appl. Math. 55 (1995), 1297-1323. Zbl0836.34041MR96g:35176
  31. [31] L.A. Peletier, D. Terman and F.B. Weissler, On the equation Δu + 1/2x · ∇u - u + f(u) = 0, Archive Rat. Mech. Anal. 94 (1986), 83-99. Zbl0615.35034MR87m:35089
  32. [32] F. Ribaud, Analyse de Littlewood Paley pour la résolution d'équations paraboliques semi-linéaires, Doctoral Thesis, University of Paris XI, January 1996. 
  33. [33] F. B. Weissler, Existence and non-existence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981), 29-40. Zbl0476.35043MR82g:35059

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