Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity

Riccardo Adami; Gianfausto Dell'Antonio; Rodolfo Figari; Alessandro Teta

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 1, page 121-137
  • ISSN: 0294-1449

How to cite

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Adami, Riccardo, et al. "Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity." Annales de l'I.H.P. Analyse non linéaire 21.1 (2004): 121-137. <http://eudml.org/doc/78609>.

@article{Adami2004,
author = {Adami, Riccardo, Dell'Antonio, Gianfausto, Figari, Rodolfo, Teta, Alessandro},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {blow-up; moment of inertia; explicit blow-up solutions; nonlinear Schrödinger equation},
language = {eng},
number = {1},
pages = {121-137},
publisher = {Elsevier},
title = {Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity},
url = {http://eudml.org/doc/78609},
volume = {21},
year = {2004},
}

TY - JOUR
AU - Adami, Riccardo
AU - Dell'Antonio, Gianfausto
AU - Figari, Rodolfo
AU - Teta, Alessandro
TI - Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 1
SP - 121
EP - 137
LA - eng
KW - blow-up; moment of inertia; explicit blow-up solutions; nonlinear Schrödinger equation
UR - http://eudml.org/doc/78609
ER -

References

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  1. [1] R. Adami, G. Dell'Antonio, R. Figari, A. Teta, The Cauchy problem for the Schrödinger equation in dimension three with a concentrated nonlinearity, Preprint, Département de mathématiques et applications, École normale supérieure, DMA-02-09, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press. Zbl1028.35137
  2. [2] Adami R, Teta A, A simple model of concentrated nonlinearity, Operator Theory Adv. Appl.108 (1999) 183-189. Zbl0967.81010MR1708796
  3. [3] Adami R, Teta A, A class of nonlinear Schrödinger equation with concentrated nonlinearity, J. Funct. Anal.180 (2001) 148-175. Zbl0979.35130MR1814425
  4. [4] Albeverio S, Gesztesy F, Högh-Krohn R, Holden H, Solvable Models in Quantum Mechanics, Springer-Verlag, New York, 1988. Zbl0679.46057MR926273
  5. [5] Cazenave T, An Introduction to Nonlinear Schrödinger Equation, Textos de Métodos Matematicos, vol. 26, IMUFRJ, Rio de Janeiro, 1993. 
  6. [6] Cazenave T, Blow-up and Scattering in the Nonlinear Schrödinger Equation, Textos de Métodos Matematicos, vol. 30, IMUFRJ, Rio de Janeiro, 1996. 
  7. [7] Ginibre J, Velo G, On a class of nonlinear Schrödinger equations, I. The Cauchy problem, general case, J. Funct. Anal.32 (1979) 1-32. Zbl0396.35028MR533218
  8. [8] Kato T, On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor.46 (1987) 113-129. Zbl0632.35038MR877998
  9. [9] Merle F, Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys.129 (1990) 223-240. Zbl0707.35021MR1048692
  10. [10] Sayapova M.R, Yafaev D.R, The evolution operator for time-dependent potentials of zero radius, Proc. Steklov Inst. Math.2 (1984) 173-180. Zbl0599.35035MR720214
  11. [11] Weinstein M.I, NLSE and sharp interpolation estimates, Comm. Math. Phys.87 (1983) 567-576. Zbl0527.35023MR691044

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