Équations d'évolution avec non linéarité logarithmique

Thierry Cazenave; Alain Haraux

Annales de la Faculté des sciences de Toulouse : Mathématiques (1980)

  • Volume: 2, Issue: 1, page 21-51
  • ISSN: 0240-2963

How to cite

top

Cazenave, Thierry, and Haraux, Alain. "Équations d'évolution avec non linéarité logarithmique." Annales de la Faculté des sciences de Toulouse : Mathématiques 2.1 (1980): 21-51. <http://eudml.org/doc/73098>.

@article{Cazenave1980,
author = {Cazenave, Thierry, Haraux, Alain},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {existence; uniqueness; regularity properties; Cauchy problem; potential; Sobolev space; truncation argument; monotonicity property; wave equation; modulus of continuity; evolution equations},
language = {fre},
number = {1},
pages = {21-51},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Équations d'évolution avec non linéarité logarithmique},
url = {http://eudml.org/doc/73098},
volume = {2},
year = {1980},
}

TY - JOUR
AU - Cazenave, Thierry
AU - Haraux, Alain
TI - Équations d'évolution avec non linéarité logarithmique
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1980
PB - UNIVERSITE PAUL SABATIER
VL - 2
IS - 1
SP - 21
EP - 51
LA - fre
KW - existence; uniqueness; regularity properties; Cauchy problem; potential; Sobolev space; truncation argument; monotonicity property; wave equation; modulus of continuity; evolution equations
UR - http://eudml.org/doc/73098
ER -

References

top
  1. [1] J.B. Baillon, T. Cazenave, M. Figueira. «Equation de Schrödinger non linéaire». C.R. Acad. Sc.Paris, 284 (1977) p. 869-872. Zbl0349.35048MR433025
  2. [2] I. Bialynicki-Birula, J. Mycielski. «Wave Equations with Logarithmic Non-linearities». Bull. Acad. Pol. Sc., XXIII (1975) p. 461-466. MR403458
  3. [3] I. Bialynicki-Birula, J. Mycielski. «Nonlinear Wave Mechanics». Annals of Physics, 100 (1976) p. 62-93. MR426670
  4. [4] H. Brezis. «Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert». North-Holland Publish Co, Amsterdam, London (1973). Zbl0252.47055MR348562
  5. [5] H. Brezis, T. Kato. «Remarks on the Schrödinger Operator with Singular Complex Potentials». J. Math. Pures. Appl.58 (1979) p. 137-151. Zbl0408.35025MR539217
  6. [6] F.E. Browder. «On Non-Linear Wave Equations». Math. Zeitschr.80 (1962) p. 249-264. Zbl0109.32102MR147769
  7. [7] T. Cazenave. «Equations de Schrödinger Non Linéaires». Proc. Roy. Soc. Edinburgh (1969)84 (1979) p. 327-346. Zbl0428.35021MR559676
  8. [8] T. Cazenave, A. Haraux. «Equations de Schrödinger avec Non Linéarité Logarithmique». C.R. Acad. Sc.Paris, 288 (1979) p. 253-256. Zbl0406.35013MR524786
  9. [9] R. Cou Rant, D. Hilbert. «Methods of Mathematical Physics». Volume II, Inter-science Publish.New-York, London (1962). Zbl0099.29504MR65391
  10. [10] J. Ginibre, G. Velo. «On a class of Non Linear Schrödinger Equations». J. Funct. Anal.32 (1979) p. 1-71. Zbl0396.35028MR533219
  11. [11] J.L. Lions. «Quelques Méthodes de Résolution de Problèmes aux Limites Non-Linéaires». Gauthier-Villars, Paris (1969). Zbl0189.40603MR259693

Citations in EuDML Documents

top
  1. E. Zuazua, Exact controllability for semilinear wave equations in one space dimension
  2. Piermarco Cannarsa, Vilmos Komornik, Paola Loreti, Well posedness and control of semilinear wave equations with iterated logarithms
  3. Piermarco Cannarsa, Vilmos Komornik, Paola Loreti, Well posedness and control of semilinear wave equations with iterated logarithms
  4. Ph. Blanchard, J. Stubbe, L. Vázquez, On the stability of solitary waves for classical scalar fields
  5. Enrique Fernández-Cara, Enrique Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations
  6. José Luis López, Jesús Montejo–Gámez, On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions
  7. Makoto Nakamura, Tohru Ozawa, Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.