- 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
.