Semi-linear diffraction of conormal waves

Melrose, Richard B. ; Sá Barreto, Antônio ; Zworski, Maciej

Astérisque, no. 240 (1996) , 138 p.

MR Zbl

@book{AST_1996__240__1_0,
     author = {Melrose, Richard B. and S\'a Barreto, Ant\^onio and Zworski, Maciej},
     title = {Semi-linear diffraction of conormal waves},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {240},
     year = {1996},
     mrnumber = {1636412},
     zbl = {0902.35004},
     language = {en},
     url = {http://www.numdam.org/item/AST_1996__240__1_0/}
}

TY  - BOOK
AU  - Melrose, Richard B.
AU  - Sá Barreto, Antônio
AU  - Zworski, Maciej
TI  - Semi-linear diffraction of conormal waves
T3  - Astérisque
PY  - 1996
IS  - 240
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1996__240__1_0/
LA  - en
ID  - AST_1996__240__1_0
ER  -

%0 Book
%A Melrose, Richard B.
%A Sá Barreto, Antônio
%A Zworski, Maciej
%T Semi-linear diffraction of conormal waves
%S Astérisque
%D 1996
%N 240
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1996__240__1_0/
%G en
%F AST_1996__240__1_0

Melrose, Richard B.; Sá Barreto, Antônio; Zworski, Maciej. Semi-linear diffraction of conormal waves. Astérisque, no. 240 (1996), 138 p. http://numdam.org/item/AST_1996__240__1_0/

Bibliographie
Cité par

[1] V. Arnol'D Wave front evolution and equivariant Morse lemma. Comm. Pure Appl. Math. 28 (1976), 557-582. | MR | Zbl | DOI

[2] M. Beals Self Spreading and Strength of Singularities for Solutions to Semilinear Equations. Ann. of Math. 118 (1983), 187-214. | MR | Zbl | DOI

[3] M. Beals Propagation of Smoothness for Nonlinear Second Order Strictly Hyperbolic Equations. Proc. Symp. Pure Math. 43 (1985), 21-45. | MR | Zbl | DOI

[4] M. Beals and G. Métivier Progressing Wave Solutions to Certain Nonlinear Mixed Problems. Duke Math. J. 53 (1986), 125-137. | MR | Zbl

[5] M. Beals and G. Métivier Reflection of Transversal Progressing Waves in Nonlinear Strictly Hyperbolic Problems. Amer. J. Math. 109 (1987), 335-366. | MR | Zbl | DOI

[6] J.-M. Bony Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup. 14, 209-246 | MR | Zbl | EuDML | Numdam | DOI

[7] J.-M. Bony Interactions des singularités pour les équations aux dérivées partielles non linéaires. Sem. Goulaouic-Meyer-Schwarz 1984. | Zbl | Numdam

[8] J. Chazarain et A. Piriou Introduction à la théorie des équations aux dérivées partielles linéaires. Bordes (Dounot), Paris, 1981. | MR | Zbl

[9] J.-Y. Chemin Interactions des trois ondes dans les équations semi-linéaires strictement hyperboliques d'ordre $2$ . Comm. P.D.E. 12 (11) (1987), 1203-1225. | MR | Zbl | DOI

[10] F. David and M. Williams Singularities of Solutions to Semilinear Boundary Value Problems Amer. J. Math. 109 (1987), 1087-1109. | MR | Zbl | DOI

[11] J.-M. Delort. Conormalité des ondes semi-linéaires le long des caustiques. Amer. Jour. Math. 113 (1991), 593-651. | MR | Zbl | DOI

[12] V. Guillemin and G. Uhlmann. Oscillatory integrals with singular symbols. Duke Math. J. 48 (1981), 251-261. | MR | Zbl | DOI

[13] L. Hörmander. Fourier integral operators I. Acta Math. 127 (1971), 79-183. | MR | Zbl | DOI

[14] L. Hörmander. The Analysis of Linear Partial Differential Operators Springer-Verlag, 1983-1985. | MR | Zbl

[15] S. Klainerman. Null condition and global existence to nonlinear wave equations. Lectures in Applied Mathematics 23, AMS, Providence, 1986, 293-326. | Zbl | MR

[16] B. Lascar. Singularités des solutions d'équations aux dérivées partielles non linéaires. C. R. Acad. Sci. Paris 287 (1978), 521-529. | MR | Zbl

[17] P. D. Lax. On Cauchy's problem for hyperbolic equations and the different ability of solutions of elliptic equations. Comm. Pure. Appl. Math. 8 (1955), 615-633. | MR | Zbl | DOI

[18] G. Lebeau. Problème de Cauchy semi-linéaire en $3$ dimensions d'espace. J. Func. Anal. 78 (1988), 185-196. | MR | Zbl | DOI

[19] G. Lebeau. Equations des ondes semi-linéaires II. Contrôle des singularités et caustiques semi-linéaires. Inv. Math. 95 (1989), 277-323. | MR | Zbl | EuDML | DOI

[20] G. Lebeau. Singularités de solutions d'équations d'ondes semi-linéaires. Ann. Scient. Éc. Norm. Sup. 4e série 25 (1992), 201-231. | MR | Zbl | EuDML | Numdam | DOI

[21] E. Leichtman Régularité microlocale pour des problèmes de Dirichlet non linéaires non caractéristiques d'ordre deux à bord peu régulier. Bull. S.M.F. 115 (1987), 457-489. | MR | Zbl | EuDML | Numdam

[22] B. Lindblad. Blow-up for solutions of $□ u = {|u|}^{p}$ with small initial data. Comm. P.D.E. 15 (6) (1990), 757-821. | MR | Zbl | DOI

[23] V. P. Maslov. The theory of perturbations and asymptotic methods. Moscow, 1965 (Russian).

[24] R. B. Melrose. Equivalence of glancing hyper surfaces. Inv. Math. 37 (1976), 165-191. | Zbl | MR | EuDML | DOI

[25] R. B. Melrose. Transformation of boundary value problems. Acta Math. 147 (1981), 149-236. | MR | Zbl | DOI

[26] R. B. Melrose. Forward Scattering by a Convex Obstacle. Comm. Pure and Appl. Math. 23 (1980), 461-499. | MR | Zbl | DOI

[27] R. B. Melrose. Semilinear waves with cusp singularities. Journées « Équations aux dérivées partielles » St. Jean-de-Montes, 1987. | MR | Zbl | EuDML | Numdam

[28] R. B. Melrose. Differential analysis on manifolds with corners. Manuscript in preparation.

[29] R. B. Melrose. Calculus of conormal distributions on manifolds with corners. Internat. Math. Res. Notices 3 (1992), 51-61. | MR | Zbl | DOI

[30] R. B. Melrose. Marked Lagrangian Distributions. preprint, 1989.

[31] R. B. Melrose and P. Piazza. Analytic $K$ -theory on manifolds with corners. Adv. in Math. 92 (1) (1992), 1-26. | MR | Zbl | DOI

[32] R. B. Melrose and N. Ritter. Interaction of Nonlinear Waves for Semilinear Wave Equations. Ann. of Math. 121 (1) (1985), 187-213. | MR | Zbl | DOI

[33] R. B. Melrose and N. Ritter. Interaction of Nonlinear Waves for Semilinear Wave Equations II. Ark. Mat. 25 (1987), 91-114. | MR | Zbl | DOI

[34] R. B. Melrose and A. Sá Barreto Semilinear Interaction of a Cusp and a Plane. Comm. In PDE 20 (5 & 6) (1995) 961-1032. | Zbl | MR | DOI

[35] R. B. Melrose and M. Taylor. Boundary Problems for the Wave Equation with Grazing and Gliding Rays. preprint, 1987.

[36] R. B. Melrose and M. Taylor. Near Peak Scattering and the Corrected Kirchhoff Approximation for a Convex Obstacle. Adv. in Math. 55 (3) (1985), 242-315. | MR | Zbl | DOI

[37] R. B. Melrose and M. Taylor. The radiation pattern of a diffracted wave near the shadow boundary. Comm. P.D.E 11 (6) (1986), 599-672. | MR | Zbl | DOI

[38] R. B. Melrose and G. Uhlmann. Lagrangian intersection and the Cauchy problem. Comm. Pure Appl. Math. 2 (1979), 483-519. | MR | Zbl | DOI

[39] J. Rauch and M. Reed. Propagation of singularities for semilinear hyperbolic wave equations in one space variable. Ann. of Math. 111 (1980), 531-552. | MR | Zbl | DOI

[40] J. Rauch and M. Reed. Singularities produced by nonlinear interaction of three progressing waves. Comm. P.D.E. 7 (9) (1982), 1117-1133. | MR | Zbl | DOI

[41] N. Ritter. Progressing wave solutions to nonlinear hyperbolic Cauchy problems. Thesis M.I.T. (June 1984). | MR

[42] A. Sá Barreto. Interaction of Conormal Waves for Fully Semilinear Wave Equations. Jour. Func. Anal. 89 (1990), 233-273. | MR | Zbl | DOI

[43] A. Sá Barreto. Second Microlocal Ellipticity and Propagation of Conormality for Semilinear Wave Equations. Jour. Func. Anal. 102 (1991), 47-71. | MR | Zbl | DOI

[44] A. Sá Barreto. Evolution of Semilinear Waves with Swallowtail Singularities. Duke Math. Journ. 75 (3) (1995), 645-710. | MR | Zbl | DOI

[45] M. Sablé-Tougeron. Régularité microlocale pour des problèmes aux limites non linéaires. Ann. Inst. Fourier 36 (1986), 39-82. | MR | Zbl | EuDML | Numdam | DOI

[46] R. Seeley Extension of $C^{\infty}$ functions defined in half space. Proc. Amer. Math. Soc. 15 (1964), 625-626. | MR | Zbl

[47] M. Williams. Interaction involving gliding rays in boundary problems for semi-linear wave equations. Duke Math. Jour. 59 (2) (1989), 365-397. | MR | Zbl

[48] C. Xu Propagation au bord des singularités pour des problèmes de Dirichlet non linéaires d'ordre deux., Actes Journées E.D.P., St. Jean-de-Monts, 1989, n° 20. | MR | Zbl | Numdam

[49] M. Zworski. High frequency scattering by a convex obstacle. Duke Math. Jour. 61 (2) (1990), 545-634. | MR | Zbl | DOI

[50] M. Zworski. Propagation of submarked lagrangian singularities. unpublished, 1990.

[51] M. Zworski. Shift of the shadow boundary in high frequency scattering. Comm. Math. Phys. 136 (1991), 141-156. | MR | Zbl | DOI