Duke Mathematical Journal

Evolution of semilinear waves with swallowtail singularities

Antônio Sá Barreto
Source: Duke Math. J. Volume 75, Number 3 (1994), 645-710.
First Page: Show Hide
Primary Subjects: 35L70
Secondary Subjects: 58G17
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077287813
Mathematical Reviews number (MathSciNet): MR1291700
Zentralblatt MATH identifier: 0827.35078
Digital Object Identifier: doi:10.1215/S0012-7094-94-07520-0

References

[1] V. I. Arnol'd, Wave front evolution and equivariant Morse lemma, Comm. Pure Appl. Math. 29 (1976), no. 6, 557–582.
Mathematical Reviews (MathSciNet): MR55:9148
Zentralblatt MATH: 0343.58003
Digital Object Identifier: doi:10.1002/cpa.3160290603
[2] V. I. Arnol'd, Elements of Classical Mechanics, Graduate Texts in Math., vol. 60, Springer-Verlag, New York, 1984.
[3] M. Beals, Regularity of nonlinear waves associated with a cusp, Microlocal analysis and nonlinear waves (Minneapolis, MN, 1988–1989), IMA Vol. Math. Appl., vol. 30, Springer, New York, 1991, pp. 9–27.
Mathematical Reviews (MathSciNet): MR92f:35034
Zentralblatt MATH: 0794.35004
[4] M. Beals, Self-spreading and strength of singularities for solutions to semilinear wave equations, Ann. of Math. (2) 118 (1983), no. 1, 187–214.
Mathematical Reviews (MathSciNet): MR85c:35057
Zentralblatt MATH: 0522.35064
Digital Object Identifier: doi:10.2307/2006959
[5] J.-M. Bony, Interaction des singulariteés pour les équations aux dérivées partielles non-linéaires, Sem. Goulaouic-Meyer-Schwartz, 1979–1980, exp. 22.
[6] J. Britt, The anatomy of low-dimensional stable singularities, Amer. Math. Monthly 92 (1985), no. 3, 183–201.
Mathematical Reviews (MathSciNet): MR86h:58018
Zentralblatt MATH: 0611.58012
Digital Object Identifier: doi:10.2307/2322873
[7] J.-M. Delort, Conormalité des ondes semi-linéaires le long des caustiques, Amer. J. Math. 113 (1991), no. 4, 593–651.
Mathematical Reviews (MathSciNet): MR93d:35006
Zentralblatt MATH: 0758.35005
Digital Object Identifier: doi:10.2307/2374842
[8] J. Duistermaat, Fourier integral operators and partial differential equations, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1974, Courant Inst.
Mathematical Reviews (MathSciNet): MR52:9008
[9] J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183–269.
Mathematical Reviews (MathSciNet): MR52:9300
Zentralblatt MATH: 0232.47055
Digital Object Identifier: doi:10.1007/BF02392165
[10] G. Lebeau, Problème de Cauchy semi-linéaire en $3$ dimensions d'espace. Un résultat de finitude, J. Funct. Anal. 78 (1988), no. 1, 185–196.
Mathematical Reviews (MathSciNet): MR89e:35101
Zentralblatt MATH: 0648.35057
Digital Object Identifier: doi:10.1016/0022-1236(88)90138-3
[11] G. Lebeau, Équations des ondes semi-linéaires. II. Contrôle des singularités et caustiques non linéaires, Invent. Math. 95 (1989), no. 2, 277–323.
Mathematical Reviews (MathSciNet): MR92j:35126b
Zentralblatt MATH: 0686.35015
Digital Object Identifier: doi:10.1007/BF01393899
[12] G. Lebeau, Singularités des solutions d'équations d'ondes semi-linéaires, Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 2, 201–231.
Mathematical Reviews (MathSciNet): MR93k:35180
Zentralblatt MATH: 0776.35088
[13] R. Melrose, Marked Lagrangian distributions, in preparation.
[14] R. Melrose, Semilinear waves with cusp singularities, Journées “Équations aux derivées partielles” (Saint Jean de Monts, 1987), École Polytech., Palaiseau, 1987, Exp. No. X, 10.
Mathematical Reviews (MathSciNet): MR89b:58209
Zentralblatt MATH: 0656.35098
[15] R. Melrose, Transformation of boundary problems, Acta Math. 147 (1981), no. 3-4, 149–236.
Mathematical Reviews (MathSciNet): MR83f:58073
Zentralblatt MATH: 0492.58023
Digital Object Identifier: doi:10.1007/BF02392873
[16] R. Melrose and N. Ritter, Interaction of nonlinear progressing waves for semilinear wave equations, Ann. of Math. (2) 121 (1985), no. 1, 187–213.
Mathematical Reviews (MathSciNet): MR86m:35005
Zentralblatt MATH: 0575.35063
Digital Object Identifier: doi:10.2307/1971196
[17] R. Melrose and N. Ritter, Interaction of progressing waves for semilinear wave equations. II, Ark. Mat. 25 (1987), no. 1, 91–114.
Mathematical Reviews (MathSciNet): MR89b:35005
Zentralblatt MATH: 0653.35058
Digital Object Identifier: doi:10.1007/BF02384437
[18] R. Melrose and P. Piazza, Analytic $K$-theory on manifolds with corners, Adv. Math. 92 (1992), no. 1, 1–26.
Mathematical Reviews (MathSciNet): MR93h:58149
Zentralblatt MATH: 0761.55002
Digital Object Identifier: doi:10.1016/0001-8708(92)90059-T
[19] R. Melrose and A. Sá Barreto, Non-linear interaction of a cusp and a plane, preprint, 1993.
[20] R. Melrose, A. Sá Barreto, and M. Zworski, Semilinear diffraction of conormal waves, preprint, 1993.
[21] J. Rauch and M. Reed, Singularities produced by the nonlinear interaction of three progressing waves; examples, Comm. Partial Differential Equations 7 (1982), no. 9, 1117–1133.
Mathematical Reviews (MathSciNet): MR83m:35097
Zentralblatt MATH: 0502.35060
Digital Object Identifier: doi:10.1080/03605308208820246
[22] A. Sá Barreto, Interactions of conormal waves for fully semilinear wave equations, J. Funct. Anal. 89 (1990), no. 2, 233–273.
Mathematical Reviews (MathSciNet): MR91h:35022
Zentralblatt MATH: 0726.35083
Digital Object Identifier: doi:10.1016/0022-1236(90)90094-2
[23] A. Sá Barreto, On the interactions of conormal waves for semilinear wave equations, Microlocal analysis and nonlinear waves (Minneapolis, MN, 1988–1989), IMA Vol. Math. Appl., vol. 30, Springer, New York, 1991, pp. 1–7.
Mathematical Reviews (MathSciNet): MR1120279
Zentralblatt MATH: 0794.35006
[24] A. Sá Barreto, Second microlocal ellipticity and propagation of conormality for semilinear wave equations, J. Funct. Anal. 102 (1991), no. 1, 47–71.
Mathematical Reviews (MathSciNet): MR92h:35144
Zentralblatt MATH: 0746.35021
Digital Object Identifier: doi:10.1016/0022-1236(91)90135-R
[25] M. Zworski, Propagation of sub-marked Lagrangian singularities, unpublished.

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?