no. 6
Problème de Cauchy pour des systèmes hyperboliques semi-linéaires
Annales de l'I.H.P. Analyse non linéaire, Tome 1 (1984) no. 6, pp. 453-478. 
@article{AIHPC_1984__1_6_453_0,
     author = {Bachelot, Alain},
     title = {Probl\`eme de {Cauchy} pour des syst\`emes hyperboliques semi-lin\'eaires},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {453--478},
     publisher = {Gauthier-Villars},
     volume = {1},
     number = {6},
     year = {1984},
     mrnumber = {778979},
     zbl = {0566.35068},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPC_1984__1_6_453_0/}
}
TY  - JOUR
AU  - Bachelot, Alain
TI  - Problème de Cauchy pour des systèmes hyperboliques semi-linéaires
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1984
SP  - 453
EP  - 478
VL  - 1
IS  - 6
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1984__1_6_453_0/
LA  - fr
ID  - AIHPC_1984__1_6_453_0
ER  - 
%0 Journal Article
%A Bachelot, Alain
%T Problème de Cauchy pour des systèmes hyperboliques semi-linéaires
%J Annales de l'I.H.P. Analyse non linéaire
%D 1984
%P 453-478
%V 1
%N 6
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1984__1_6_453_0/
%G fr
%F AIHPC_1984__1_6_453_0
Bachelot, Alain. Problème de Cauchy pour des systèmes hyperboliques semi-linéaires. Annales de l'I.H.P. Analyse non linéaire, Tome 1 (1984) no. 6, pp. 453-478. http://www.numdam.org/item/AIHPC_1984__1_6_453_0/

[1] A. Bachelot, Problème de Cauchy pour des systèmes de Klein-Gordon-Schroedinger. C. R. Acad. Sc. Paris, t. 296, 1983, p. 525-528. | MR | Zbl

[2] J.B. Baillon et J.M. Chadam, The Cauchy problem for the coupled Schroedinger-Klein-Gordon equations ; in Contemporary Developments in Continuum Mechanics | Zbl

and Partial differential equations, G. M. de la Penha, L. A. Medeiros (Eds), North-Holland Publishing Company, 1978.

[3] M. Balabane, H. Emani-Rad, Pseudodifferential parabolic systems in Lp(Rn) ; in « Contributions to nonlinear partial differential equations », C. Bardos, A. Damlamian, J. I. Diaz, J. Hernandez (Eds), Research Notes in Maths 89, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1983. | MR | Zbl

[4] Ph. Brenner, The Cauchy problem for systems in Lp and Lp,α, Ark. Mat., t. 11, 1973, p. 75-101. | MR | Zbl

[5] Ph. Brenner, V. Thomee, L.B. Wahlbin, Besov spaces and applications to difference methods for initial value problems, Lecture Notes in Math., t. 434, Springer-Verlag, Berlin, Heidelberg, New-York, 1975. | MR | Zbl

[6] J. Chadam, Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension ; J. Func. Anal., t. 13, 1973, p. 173-184. | MR | Zbl

[7] J. Chadam, Asymptotic behaviour of equations arising in quantum field theory ; J. Applic. Anal., t. 3, 1973, p. 377-402. | MR | Zbl

[8] J. Chadam, R. Glassey, On the Maxwell-Dirac equations with zero magnetic field and their solutions in two space dimensions ; J. Math. Anal. and Appl., t. 53, 1976, p. 495-507. | MR | Zbl

[9] J. Chadam, R. Glassey, On certain global solutions of the Cauchy problem for the (classical) coupled Klein-Gordon-Dirac equations in one and three space dimensions ; Arch. Rat. Mech. Anal., t. 54, 1974, p. 223-237. | MR | Zbl

[10] Y. Choquet-Bruhat, Solutions globales des equations de Maxwell-Dirac-Klein-Gordon (masses nulles) ; C. R. Acad. Sc. Paris, t. 292, 1981, p. 153-158. | MR | Zbl

[11] G. Da Prato, E. Giusti, Equazioni di Schrödinger e delle onde per l'operatore di Laplace iterato in Lp(Rn); Ann. Mat. Pura e Appl., t. 76, 1967, p. 377-397. | MR | Zbl

[12] I. Fukuda, M. Tsutsumi, On coupled Klein-Gordon-Schrödinger equations, I, Bull. Sci. Engeg. Res. Lab. Waseda Univ., t. 69, 1975, p. 51-62. | MR

[13] I. Fukuda, M. Tsutsumi, On coupled Klein-Gordon-Schrödinger equations, II, J. Math. Anal. and Applic., t. 66, 1978, p. 358-378. | MR | Zbl

[14] I. Fukuda, M. Tsutsumi, On coupled Klein-Gordon-Schrödinger equations, III, Math. Japonica, t. 24, n° 3, 1979, p. 307-321. | MR | Zbl

[15] L. Gross, The Cauchy problem for the coupled Maxwell-Dirac equations, Comm. Pure and Appl. Math., t. 19, 1966, p. 1-15. | MR | Zbl

[16] E.J. Holder, JR, On the existence, scattering, and blow up of solutions to systems of nonlinear Schrödinger equations ; Indiana Univ. Math. J., t. 30, 1981, p. 653-673. | MR | Zbl

[17] L. Hörmander, Estimates for translation invariant operators in Lp-spaces ; Acta Math., t. 104, 1960, p. 93-140. | MR | Zbl

[18] W. Littman, The wave operator and Lp norms ; J. Math. Mech., t. 12, 1963, p. 55-68. | MR | Zbl

[19] B. Marshall, W. Strauss, S. Wainger, Lp-Lp' estimates for the Klein-Gordon equation; J. Math. Pures et Appl., t. 59, 1980, p. 417-440. | MR | Zbl

[20] J. Peral, Lp estimates for the wave equation ; J. Func. Anal., t. 36, 1980, p. 114-145. | MR | Zbl

[21] M. Reed, Abstract nonlinear wave equations ; Lecture Notes in Math., t. 507, Springer-Verlag, 1976. | Zbl

[22] M. Reed, B. Simon, Methods of modern mathematical physics, Vol. 2, Fourier analysis, Self adjointness, Academic Press, New York. 1975. | Zbl

[23] J. Segal, Nonlinear semi-groups ; Ann. Math., t. 78, 1963, p. 339-364. | MR | Zbl

[24] S. Sjöstrand, On the Riesz means of solutions of Schrödinger equation ; Ann. Scuola Norm. Sup. Pisa, t. 24, 1970, p. 331-348. | Numdam | MR | Zbl