Équations de champs non linéaires : des solutions non nécessairement bornées
Journées équations aux dérivées partielles (1992), article no. 20, 13 p. 
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     author = {Beals, Michael and Bezard, Max},
     title = {\'Equations de champs non lin\'eaires : des solutions non n\'ecessairement born\'ees},
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     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {20},
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     year = {1992},
     publisher = {Ecole polytechnique},
     doi = {10.5802/jedp.438},
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     url = {https://www.numdam.org/articles/10.5802/jedp.438/}
}
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Beals, Michael; Bezard, Max. Équations de champs non linéaires : des solutions non nécessairement bornées. Journées équations aux dérivées partielles (1992), article  no. 20, 13 p.. doi: 10.5802/jedp.438

[1] A. Bachelot - Problème de Cauchy global pour les systèmes de Dirac - Klein - Gordon. Ann. IHP Phys. Theor. 48 (1988) 383-428. | Numdam | MR | Zbl

[2] M. Beals - Lp boundedness of Fourier integral operators. Memoirs AMS 264 (1982). | Zbl

[3] M. Beals, M. Bezard - Low regularity local solutions for field equations. preprint. | Zbl

[4] M. Bezard - Une généralisation d'une inégalité de Strichartz. Note CRAS à paraître.

[5] J. Björken, S. Drell - Relatvistic quantum mechanics. Mc Graw Hill.

[6] J.M. Bony - Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. ENS 14 (1981) 209-246. | Numdam | MR | Zbl

[7] J.M. Bony - Interaction des singularités. séminaire Goulaouic - Schwartz 1981-1982. | Numdam | Zbl

[8] J.M. Bony - Interaction des singularités pour des équations de Klein - Gordon non linéaires. séminaire Goulaouic - Meyer - Schwartz 1983-1984. | Numdam | Zbl

[9] P. Brenner - On Lp - Lp' estimates for the wave equation. Math. Z 145 (1975) 251-254. | MR | Zbl

[10] P. Brenner, W. Von Wahl - Global classical solutions of non linear wave equations. Math. Z 176 (1981) 87-121. | MR | Zbl

[11] J.Y. Chemin - Interaction de 3 ondes dans les équations semi-linéaires strictement hyperboliques. CPDE 12 (1987) 1203-1225. | MR | Zbl

[12] J.Y. Chemin - Calcul symbolique bilinéaire et interaction contrôlée dans les équations aux dérivées partielles non linéaires strictement hyperboliques. Bull. SMF 116 (1988) 341-383. | Numdam | MR | Zbl

[13] J. Ginibre, G. Velo - The Cauchy problem for coupled Yang - Mills and scalar fields in Lorentz gauge. Ann. IHP Phys. Theor. 36 (1982) 59-78. | Numdam | MR | Zbl

[14] C. Greiner - Relativistic quantum mechanics. Springer.

[15] B. Hanouzet, J.L. Joly - Applications bilinéaires compatibles avec un système hyperbolique. C.R. Acad. Sci. Paris 301 (1985) 491-494. | MR | Zbl

[16] L. Hörmander - The analysis of linear partial differential operators. Springer 4 Vol. | Zbl

[17] L. Hörmander - Nonlinear hyperbolic differential equations. Course in lund (1988).

[18] T. Hughes, T. Kato, J. Marsden - Well posed quasi linear second order hyperbolic systems with applications to nonlinear elastodynamics and general relativity. Archive Rat. Mech. Anal. 63 (1977) 273-294. | MR | Zbl

[19] L. Kapitanski - The Cauchy problem for a semi-linear wave equation. preprint.

[20] C. Kenig, A. Ruiz, C. Sogge - Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators. Duke Math. J. Vol. 55 (1987) 329-347. | MR | Zbl

[21] S. Klainerman - The null condition and global existence for non linear waves. AMS Lect. Appl. Math. 23 (1986) 293-325. | MR | Zbl

[22] S. Klainerman, M. Machedon - Space-time estimates for null forms and the local existence theorem. Preprint (1991). | Zbl

[23] H. Lindblad - Blow-up for solutions of □ u = |u|p with small initial data. CPDE 15 (1990) 757-821. | MR | Zbl

[24] B. Marshall, W. Strauss, S. Wainger - Lp - Lq estimates for the Klein - Gordon equation. JMPA 59 (1980) 417-440. | MR | Zbl

[25] R. Melrose, Ritter - Interaction of progressing waves for semi-linear wave equation I Ann. Math. 121 (1985) 149-236. | MR | Zbl

[26] R. Melrose, Ritter - Interaction of progressing waves for semi-linear wave equation II Arkiv. for Math. 25 (1987) 91-114. | MR | Zbl

[27] J. Peral - Lp estimates for the wave equation. JFA 36 (1980) 114-145. | MR | Zbl

[28] G. Ponce, T. Sideris - Local regularity of non linear wave equations in three space dimensions. to appear CPDE. | Zbl

[29] A. Seeger, C. Sogge, E. Stein - Regularity properties of Fourier integral operators. Ann. Math. Vol. 134 (1991) 231-251. | MR | Zbl

[30] I. Segal - Nonlinear semi-groups. Ann. Math. 78 (1963) 339-364. | MR | Zbl

[31] J. Shatah, M. Struwe - Regularity results for nonlinear wave equations. Preprint. | Zbl

[32] C. Sogge - Propagation of singularities and maximal functions in the plane. Inv. Math. 104 (1991) 349-376. | MR | Zbl

[33] C. Sogge, E. Stein - Averages over hypersurfaces smoothness of generalized Radon transforms. J. Anal. Math. Vol 54 (1990) 165-188. | MR | Zbl

[34] E. Stein - Beijing lectures in harmonic analysis. Princeton Univ. Press. | Zbl

[35] W. Strauss - Nonlinear wave equations. CBMS conference AMS 73.

[36] H. Strichartz - Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave. Duke Math. J. Vol. 44 (1977) 705-714. | MR | Zbl

[37] Y. Zheng - Regularity of weak solutions to a two dimensional modified Dirac - Klein - Gordon system of equations. Preprint MSRI (1991). | Zbl

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