- Partial Differential Equations
- Applied Mathematics
(1) Dispersive nonlinear geometric optics, J. Math. Phys., 38(1997),1484-1523 (with P. Donnat), ps version.
(2) Modelling the dispersion of Light, in Singularities and Oscillations, IMA Volumes in Mathematics and it Applications Vol. 91, Springer-Verlag 1997, pp. 17-36 (with P. Donnat), ps version
(3) Diffractive Nolinear Optics I, Seminaire Equations aux Derivees Partielles 1995-1996, Ecole Polytechnique, Paris (with P. Donnat, J.-L. Joly, and G. Metivier), ps version.
(4) Global solvability of the Maxwell-Bloch equations from nonlinear optics, Arch. Rat. Mech. Anal. (136)(1996),291-303. (with P. Donnat), ps version.
(5) Dense oscillations for the Euler equations II, pp. 425-430 in Hyperbolic Problems: Theory Numerics, Applications, eds. J. Glimm, M.J. Graham, J.W. Grove, B.J. Plohr., World Scientific, 1996, (with J.-L. Joly, and G. Metivier), ps version.
(6) Global solutions of the anharmonic oscillator model in nonlinear optics, SIAM J. Appl. Anal. 27(1996) 903-913. (with J.-L. Joly, and G. Metivier), ps version.
(7) Hyperbolic Partial Differential Equations and Geometric Optics, To appear in American Mathematics Society Graduate Texts in Mathematics series. Sorry, no longer on my web page.
(8) Diffractive nonlinear geometric optics with rectification, Indiana U. Math. J. 47(1998) 1167-1242, (with J.-L. Joly, and G. Metivier), ps version.
(9) Global existence for Maxwell's equations in a ferromagnetic medium, (with J.-L. Joly, and G. Metivier), Ann. Inst. Fourier Phys. Theor. Physique Th\'eorique, ps version.
(10) Dense oscillations for the Euler equations II, (with J.-L. Joly, and G. Metivier), in {\it Hyperbolic Problems: Theory, Numerics, Applications} eds. J. Glimm, M.J. Graham, J.W. Grove, B.J. Plohr, World Scientific 1994, 425-431, ps version.
(11) Optique geometrique resonante et tissus, (with J.-L. Joly and G. M\'etivier), Proceedings of Colloque Toulouse. 19p, ps version.
(12) Nonlinear hyperbolic smoothing at a focal point, (with J.-L. Joly and G. M\'etivier), Mich. Math. J., to appear, 17p, ps version.
(13) Validity of nonlinear geometric optics with times growing logarithmically, (with D. Lannes), Proc. Amer. Math. Soc., 2000. pdf version, or ps version.
(14) Diffractive short pulse asymptotics for nonlinear wave equations, (with D. Alterman), Physics Letters A 264(5):390-395, 2000, pdf version, or ps version.
(15) Nonlinear geometric optics for short pulses, (with D. Alterman), Comm. PDE, 26p. pdf version, or ps version.
(16) The linear diffractive pulse equation, (with D. Alterman), Methods and Applications of Analysis, pdf version, or ps version.
(17) Focusing of spherical nonlinear pulses in R^{1+3}, (with R. Carles), Proc. Amer. Mat. Soc., pdf version, or ps version.
(18) Diffractive Nonlinaer Geometric Optics for Short Pulses, (with D. Alterman), SIAM J. Math Anal., pdf version.
(19) Focussing of sherical nonlinear pulses R^{1+3} II. Nonlinear Caustic, (with R. Carles), Revista Matematica Iberoamericana (2004)815-864, pdf version, or ps version.
(20) Group velocity at smooth points of the characteristic variety, Colloque en l'honneur de J.-M. Bony, ed. G. Lebeau, Asterix, pdf version, or ps version.
(21) Real and complex regularity are equivalent for hyperbolic characteristic varieties, (with G. M\'etivier), Differential and Integral Equations, pdf version, or ps version.
(22) Focusing of spherical nonlinear pulses in R^{1+3} III. Sub and supercritical cases, (with R. Carles), Tohouko Math. J(2004)393-410., pdf version, or ps version.
(23) Intuitive and counterintuitive energy flux, Arch. Rat. Mech. Anal., 83-110, pdf version.
(24) Review of Wave Motion, by J. Billingham and A.C. King, AMS Monthly, April 2003, pp. 253-258. pdf version.
(25) Uniqueness and nonuniuqueness for nonsmooth divergence free transport, (with F. Colombini and T. Luo), Seminaire-EDP, Ecole Polytechnique, 2003. pdf version.
(26) The time integrated far field for Maxwell's and D'Alembert's equations, (with G. Mourou), Proc. AMS(2005), 851-858. pdf version.
(27) Hyperbolic domains of determinacy and Hamilton- Jacobi equation, (with J.-L. Joly and G. Metivier), J. Hyperbolic PDE(2005), 713-744. pdf version.
(28) A note on two dimensional transport with bounded divergence, (with F. Colombini and G. Crippa), Comm. PDE, 2005 pdf version.
(29) Nonlinear asymptotics for hyperbolic internal waves of small width, (with O. Gues), J. Hyperbolic DE, 269-295, pdf version.
(30) C^1 Measure respecting maps preserve BV iff they have bounded derivative, (with F. Colombini and T. luo), preprint, pdf version.
(31) Precise finite speed with bare hands, Methods and Applications of Analysis, 2006, 267-277, pdf version.
(32) Finite speed for symmetrizable hyperbolic systems, Jour. Hyp. PDE, 2005, 267-277. pdf version.
(33) Hyperbolic multipliers are translations, (with O. Gues) Comm PDE, 2006, 431-433, pdf version.
(34) Regularity of functions smooth along foliations and elliptic regularity, (with M. Taylor), J. Funct. Anal.(2005)74-93. ps version.
(35) The order of accuracy of quadrature formulae for periodic functions, (with A. Kurganov), in Phase Space Analysis of PDEs 2007, eds. A. Bove, D. Del Santo, M.K.V. Murthy, Progress in nonlinear differential equations and their applications, Birkhauser, to appear . pdf version.
(36) A travers un prism, in Lecons de Mathematiques d'Aujourd'hui vol III, eds E. Charpentier and N. Nikolski, Cassini Pubs., Paris, pp. 35-68. pdf version.
(37) Exponential growth for the wave equation with compact time-periodic positive potential, (with F. Colombini and V. Petkov). Comm. Pure Appl. Math., preprint, pdf version.
(38) Quadrature estimates for multiple integrals, (with M. Taylor), Houston J. Math., preprint. pdf version.
(39) Diffractive behavior of the wave equation in periodic media: weak convergence analysis, (with G. Allaire and Mariapia Palombaro), Annali di Matematica Pura ed Applicada, preprint , pdf version.
(40) Diffractive geometric optics for Bloch wave packets, (with G. Allaire and Mariapia Palombaro), preprint, pdf version.
(41) Precise finite speed and uniqueness in the Cauchy Problem for symmetrizable hyperbolic systems, Trans. AMS preprint, pdf version.
(42) Dispersive stabilization, (with G. Metivier), Bull. London Math. Soc. 2010, pdf version.
(43) Smooth localized parametric resonance for wave equations, (with F. Colombini), J. Reine Angew. Math.(2008)1--14, preprint, pdf version.
(44) A simple example of parametric resonance for the wave equation, (with F. Colombini), Serdica Mathematics Journal, (2008)55-66 , preprint, pdf version.
(45) Hyperbolic systems modeling currency hoarding, (with E. Quercioli), Communications in Mathematical Analysis, preprint, pdf version.
(46) Optimal focussing for monochromatic scalar and electromagnetic waves, submitted, arxiv version.
(47) Guy Metivier Colloque Slides.
(48) Incoming and disappearing solutions of Maxwell's equations, (with F. Colombini and V. Petkov), Procedings of the AMS, to appear, arxiv version.
(49) The analysis of matched layers, (with L. Halpern), to appear, arxiv version.
(50) Stability of transonic shock solutions for one-dimensional Euler-Poisson equations, (with T. Luo, Chunjing Xie, and Zhouping Xin), Archiv. Rat. Mech. Anal., to appear, arxiv version.
(51) Rays, plane waves, and control, slides .