Dernière modification/last modified : 19/04/2012.
Publications
J'ai présenté certains de ces articles en séminaires. Quelques textes d'exposés sont disponibles dans la rubrique textes d'exposés.
Some of these papers have been presented in seminars. You can find in the link "Slides of seminars" some of these presentations.
R. Côte and H. Zaag. Construction of a multi-soliton blow-up solution to the semilinear wave equation in one space dimension. Comm. Pure Appl.
Math., (2012), to appear. on arxiv.org.
F. Merle and H. Zaag. Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Bull. Sci. Math. 135 (2011), 353-373. on arxiv.org, doi:10.1016/j.bulsci.2011.03.001.
M.A. Ebde and H. Zaag. Construction and stability of a blow up solution for a nonlinear heat equation with a gradient term. Bol. Soc. Esp. Mat. Apl. SeMA 53 (2011), 5-21. pdf.
F. Merle and H. Zaag. Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Duke Math. J. (2012), to appear. on arxiv.org.
F. Merle and H. Zaag. Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Séminaire sur les Équations aux Dérivées
Partielles, 2009--2010, Exp. No. 11, 10 pp., École Polytech., Palaiseau, 2010. pdf.
on the website of cedram.org.
M.A. Hamza and H. Zaag. A Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations in the critical case. J. Hyperbolic Differ. Equ. (2012), to appear. on arxiv.org.
F. Merle, H. Zaag. On characteristic points at blow-up for a semilinear wave equation in one space dimension. In Singularities in Nonlinear Problems, Kyoto 2009. pdf.
F. Merle and H. Zaag. Existence and classification of characteristic points for a
semilinear wave equation in one space dimension. Amer. J. Math. (2012), to appear. on arxiv.org.
M.A. Hamza and H. Zaag. A Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations. (2009), submitted. on arxiv.org.
S. Khenissy, Y Rebai, and H. Zaag. Continuity of the blow-up profile with respect to initial data and to
the blow-up point for a semilinear heat equation. Ann. Inst. H. Poincaré
Anal. Non Linéaire 28 (2011), no. 1, 1-26. pdf, doi:10.1016/j.anihpc.2010.09.006.
N. Nouaili and H. Zaag. A Liouville theorem for vector-valued semilinear heat equations with no gradient structure and applications to blow-up. Trans. Amer. Math. Soc. 362 (2010), no. 7, 3391-3434.
pdf, on the website of the AMS.
N. Masmoudi and H. Zaag. Blow-up profile for the complex Ginzburg-Landau equation. J. Funct. Anal. 225 (2008), 1613-1666. pdf, on the website of jfa.
F. Merle and H. Zaag. Openness of the set of non characteristic points and regularity of the blow-up curve for the 1 d semilinear wave equations. Comm. Math. Phys. 282 (2008), 55-86. pdf,
on the website of CMP.
F. Merle and H. Zaag. Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. J. Funct. Anal. 253 (2007), 43--121. pdf, on the website of jfa.
H. Zaag. Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation. Duke Math. J. 133 (2006), no. 3, 499--525. pdf.
L. Corrias, B. Perthame and H. Zaag. $L^p$ and $L^\infty$ a priori estimates for some chemotaxis models and applications to the Cauchy problem. The mechanism of the spatio-temporal pattern arising in reaction diffusion system, Kyoto 2004. pdf.
F. Merle and H. Zaag. On growth rate near the blow-up surface for semilinear wave equations. Internat. Math. Res. Notices (2005), no. 19, 1127--1155. pdf.
F. Merle and H. Zaag. Determination of the blow-up rate for a critical semilinear wave equation. Math. Annalen 331 (2005), no. 2, 395--416.
pdf.
L. Corrias, H. Perthame and H. Zaag. Global solutions of some chemotaxis and angiogenesis systems in high space dimensions. Milan J. Math. 72 (2004), 1--28. pdf.
F. Merle and H. Zaag. Determination of the blow-up rate for the semilinear wave equation.
Amer. J. Math. 125 (2003), no. 5, 1147--1164. pdf.
L. Corrias, B. Perthame and H. Zaag. A chemotaxis model
motivated by angiogenesis. C. R. Math. Acad. Sci. Paris 336 (2003),
no. 2, 141--146. pdf.
P. Groisman, J.D. Rossi and H. Zaag. On the dependence of the
blow-up time with respect to the initial data in a semilinear parabolic
problem. Comm. Partial Differential Equations (2003), no. 3-4, 737--744. pdf.
H. Zaag. Regularity of the blow-up set and singular behavior for semilinear heat equations. Mathematics &
mathematics education (Bethlehem, 2000), 337--347, World Sci. Publishing, River Edge, NJ, 2002. pdf.
H. Zaag. One dimensional behavior of singular ${N}$ dimensional solutions
of semilinear heat equations. Comm. Math. Phys. 225
(2002), no. 3, 523--549. pdf.
H. Zaag. On the regularity of the blow-up set for semilinear heat equations. Ann. Inst. H. Poincaré
Anal. Non Linéaire 19 (2002), no. 5, 505--542. pdf.
F. Merle and H. Zaag. Uniform blow-up estimates
for nonlinear heat equations and applications. IMS Conference on
Differential Equations from Mechanics (Hong Kong, 1999). Methods
Appl. Anal. 8 (2001), no. 4, 551--556. pdf.
F. Merle and H. Zaag. ODE type behavior of blow-up solutions of
nonlinear heat equations. Discrete Contin. Dyn. Syst. 8 (2002),
no. 2, 435-450. pdf.
H. Zaag. A Liouville theorem and blow-up behavior for a vector-valued
nonlinear heat equation with no gradient structure. Comm. Pure Appl.
Math., 54 (2001), no. 1, 107--133. pdf.
C. Fermanian Kammerer and H. Zaag. Boundedness up to blow-up
of the difference between two solutions to a semilinear heat equation.
Nonlinearity 13 (2000), no. 4, 1189--1216. pdf.
C. Fermanian Kammerer, F. Merle and H. Zaag. Stability of the blow-up
profile of non-linear heat equations from the dynamical system point of
view. Math. Ann. 317 (2000), no. 2, 347--387. pdf.
F. Merle and H. Zaag. A Liouville theorem for vector-valued nonlinear
heat equations and applications. Math. Ann. 316 (2000), no. 1, 103--137. pdf.
H. Zaag. A remark on the energy blow-up behavior for nonlinear heat
equations. Duke Math. J. 103 (2000), no. 3, 545--556. pdf.
F. Merle and H. Zaag. Estimations uniformes à l'explosion
pour les équations de la chaleur non linéaires et applications.
Séminaire sur les Équations aux Dérivées
Partielles, 1996--1997, Exp. No. XIX, 10 pp., École Polytech., Palaiseau, 1997. pdf.
F. Merle and H. Zaag. Refined uniform estimates at blow-up and applications
for nonlinear heat equations.
Geom. Funct. Anal. 8 (1998), no. 6,
1043--1085. pdf.
F. Merle and H. Zaag. Optimal estimates for blowup rate and behavior
for nonlinear heat equations.
Comm. Pure Appl. Math. 51 (1998),
no. 2, 139--196. pdf.
F. Merle and H. Zaag. Reconnection of vortex with the boundary and
finite time quenching.
Nonlinearity 10 (1997), no. 6, 1497--1550. pdf.
H. Zaag. Blow-up results for vector-valued nonlinear heat equations
with no gradient structure. Ann.Inst. H. Poincaré Anal. Non Linéaire
15 (1998), no. 5, 581--622. pdf.
F. Merle and H. Zaag. Stability of the blow-up profile for equations
of the type $u\sb t=\Delta u+\vert u\vert \sp {p-1}u$. Duke Math. J.
86 (1997), no. 1, 143--195. pdf.
F. Merle and H. Zaag. Stabilité du profil à l'explosion
pour les équations du type $u\sb t=\Delta u+\vert u\vert \sp {p-1}u$.
C. R. Acad. Sci. Paris Sér. I Math.
322 (1996), no. 4, 345--350. pdf.
Pour visualiser les fichiers pdf, installer Acrobat
Reader.
