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Cazenave, Thierry; Haraux, Alain

Equations d’évolution avec non linearite logarithmique. (French) Zbl 0411.35051

Ann. Fac. Sci. Toulouse, V. Ser., Math. 2, 21-51 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0411.35051

Cited in 98 Documents

MSC:

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L05 Wave equation
35A25 Other special methods applied to PDEs

Keywords:

existence; uniqueness; regularity properties; Cauchy problem; potential; Sobolev space; truncation argument; monotonicity property; wave equation; modulus of continuity; evolution equations
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\textit{T. Cazenave} and \textit{A. Haraux}, Ann. Fac. Sci. Toulouse, Math. (5) 2, 21--51 (1980; Zbl 0411.35051)
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References:

[1] Baillon, J.B., Cazenave, T., Figueira, M.. «Equation de Schrödinger non linéaire». C.R. Acad. Sc.Paris, 284 (1977) p. 869-872. · Zbl 0349.35048
[2] Bialynicki-Birula, I., Mycielski, J.. «Wave Equations with Logarithmic Non-linearities». Bull. Acad. Pol. Sc., XXIII (1975) p. 461-466.
[3] Bialynicki-Birula, I., Mycielski, J.. «Nonlinear Wave Mechanics». Annals of Physics, 100 (1976) p. 62-93.
[4] Brezis, H.. «Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert». North-Holland Publish Co, Amsterdam, London (1973). · Zbl 0252.47055
[5] Brezis, H., Kato, T.. «Remarks on the Schrödinger Operator with Singular Complex Potentials». J. Math. Pures. Appl.58 (1979) p. 137-151. · Zbl 0408.35025
[6] Browder, F.E.. «On Non-Linear Wave Equations». Math. Zeitschr.80 (1962) p. 249-264. · Zbl 0109.32102
[7] Cazenave, T.. «Equations de Schrödinger Non Linéaires». Proc. Roy. Soc. Edinburgh (1969)84 (1979) p. 327-346. · Zbl 0428.35021
[8] Cazenave, T., Haraux, A.. «Equations de Schrödinger avec Non Linéarité Logarithmique». C.R. Acad. Sc.Paris, 288 (1979) p. 253-256. · Zbl 0406.35013
[9] Rant, R. Cou, Hilbert, D.. «Methods of Mathematical Physics». Volume II, Inter-science Publish.New-York, London (1962). · Zbl 0099.29504
[10] Ginibre, J., Velo, G.. «On a class of Non Linear Schrödinger Equations». J. Funct. Anal.32 (1979) p. 1-71. · Zbl 0396.35028
[11] Lions, J.L.. «Quelques Méthodes de Résolution de Problèmes aux Limites Non-Linéaires». Gauthier-Villars, Paris (1969). · Zbl 0189.40603
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