Dernière modification/last modified : 30/3/2024.
Publications
J'ai présenté certains de ces articles en séminaire. 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.
S. Latrach, E. Ogier-Denis, N. Vauchelet and H. Zaag.
Mathematical study of the spread and blocking in
inflammatory bowel disease.
(2024), submitted.
HAL: 04441859.
S. Al-Ali, J. Chaussard, S. Li-Thiao-Té, E. Ogier-Denis,
A. Percy-du-sert, X. Tréton and H. Zaag.
Detection of ulcerative colitis lesions from weakly annotated colonoscopy videos using bounding boxes.
Gastrointest. Disord.
(2024), 6, 292-307.
doi:10.3390/gidisord6010020,
techrxiv.24566263.
V.T. Nguyen, N. Nouaili and H. Zaag.
Construction of type I-Log blowup for the Keller-Segel system in dimensions 3 and 4.
(2023), submitted.
arXiv:2309.13932.
T.S. Nguyen, M. Luong, J. Chaussard, A. Beghdadi, H. Zaag and T. Le-Tien
A Quality-Oriented Database for Video Capsule
Endoscopy
IEEE 11TH European workshop on visual information processing (EUVIP)
(2023), Gjovik, Norway, pp. 1-6.
doi:10.1109/EUVIP58404.2023.10323071.
T. Roy and H. Zaag.
The blow-up rate for a loglog non-scaling invariant semilinear wave equation (2023), submitted.
arXiv:2308.12220.
G.K. Duong, N. Nouaili and H. Zaag.
Flat blow-up solutions for the complex Ginzburg Landau equation (2023), submitted.
arXiv:2308.02297.
M. Benjemaa, A. Jrajria and H. Zaag.
Rescaling method for blow-up solutions of nonlinear wave equations (2023), submitted.
arXiv:2309.05358.
A. Rebai, L. Boukhris, R. Toujani, A. Gueddiche, F. A. Banna,
F. Souissi, A. Lasram, E. Ben Rayana and H. Zaag.
Unsupervised physics-informed neural network in
reaction-diffusion biology models (Ulcerative colitis and Crohn's
disease cases) A preliminary study (2023), submitted.
arXiv:2302.07405.
T. -S. Nguyen, J. Chaussard, M. Luong, H. Zaag and A. Beghdadi.
A No-Reference Measure for Uneven Illumination
Assessment on Laparoscopic Images.
2022 IEEE International Conference on Image Processing (ICIP),
(2022), pp. 4103-4107.
doi:10.1109/ICIP46576.2022.9897302.
Y.C. Huang and H. Zaag.
Gradient profile for the reconnection of vortex
lines with the boundary in type-II superconductors.
J. Evol. Equ.
24, 2 (2024).
doi:10.1007/s00028-023-00932-9.
arXiv:2210.14773.
G.K. Duong, N. Nouaili and H. Zaag.
Modulation theory for the flat blowup solutions
of nonlinear heat equation
Commun. Pure Appl. Anal. 22
(2023), 2925-2959.
doi:10.3934/cpaa.2023094,
arXiv:2206.04378.
F. Merle and H. Zaag.
On degenerate blow-up profiles for the
subcritical semilinear heat equation
J. Eur. Math. Soc.
(2023), to appear.
arXiv:2205.06795.
J.P. Eckmann, F. Hassani and H. Zaag.
Instabilities Appearing in Effective Field
theories: When and How?
Nonlinearity 36
(2023), 4844.
doi:10.1088/1361-6544/ace769,
arXiv:2205.01055.
B. Abdelhedi and H. Zaag.
Refined blow-up asymptotics for a perturbed
nonlinear heat equation with a gradient and a non-local term.
J. Math. Anal. Appl. 515
(2022), 126447.
doi:10.1016/j.jmaa.2022.126447,
arXiv:2112.03039.
G.K. Duong, T. Ghoul and H. Zaag.
Gradient blowup profile for the semilinear heat equation.
Discrete Contin. Dyn. Syst., 44(4) (2024), 997--1025.
doi:10.3934/dcds.2023136,
arXiv:2109.03497.
P. Lin and H. Zaag.
Feedback controllability for blowup points of
heat equation.
J. Math. Pures Appl., 168 (2022), 65-107.
doi:10.1016/j.matpur.2022.09.010,
arXiv:2107.02436.
G.K. Duong, T. Ghoul, N. Kavallaris and H. Zaag.
Blowup solutions for the shadow limit model of
singular Gierer-Meinhardt system with critical parameters.
J. Differential Equations 336
(2022), 73--125.
doi: 10.1016/j.jde.2022.07.010,
arXiv:2106.07481.
S. Al-Ali, J. Chaussard, S. Li-Thiao-Té, E. Ogier-Denis,
A. Percy-du-sert, X. Tréton and H. Zaag.
P015 Detection of endoscopic lesions from
limited quality annotations in colonoscopy videos.
Journal of Crohn s and Colitis 16 (2022), 142--144.
doi: 10.1093/ecco-jcc/jjab232.144
S. Al-Ali, J. Chaussard, S. Li-Thiao-Té, E. Ogier-Denis,
A. Percy-du-sert, X. Tréton and H. Zaag.
Automatic bleeding and ulcer detection from limited quality annotations in ulcerative colitis.
Gastroenterology 162(3) (2022), S19-S20.
doi: 10.1053/j.gastro.2021.12.045
F. Merle and H. Zaag.
Behavior rigidity near non-isolated blow-up
points for the semilinear heat equation.
Int. Math. Res. Not. 20
(2022), 16196-16260.
doi:10.1093/imrn/rnab169,
arXiv:2103.12795.
M.A. Hamza and H. Zaag.
The blow-up rate for a non-scaling invariant
semilinear heat equation.
Arch. Rat. Mech. Anal., 87-125, (2022).
doi:10.1007/s00205-022-01760-w,
arXiv:2102.00768.
M.A. Hamza and H. Zaag.
The blow-up rate for a non-scaling invariant
semilinear wave equations in higher dimensions.
Nonlinear Analysis 212
(2021), 112445.
already online:
doi:10.1016/j.na.2021.112445,
arXiv:2012.05374.
G.K. Duong, N. Nouaili and H. Zaag.
Refined asymptotic for the blow-up solution of
the Complex Ginzburg-Landau equation in the subcritical case.
Ann. I. H. Poincaré - AN, 39 (2022), 41-85.
doi:10.4171/AIHPC/2,
HAL:03090581v1.
G.K. Duong, N. Kavallaris and H. Zaag.
Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer-Meinhardt system.
Math. Models Methods Appl. Sci.
Vol. 31, No. 7 (2021) 1469-1503.
doi:10.1142/S0218202521500305,
arXiv:2010.09867.
B. Abdelhedi and H. Zaag.
Single point blow-up and final profile for a
perturbed nonlinear heat equation with a gradient and a non-local
term.
Discrete Contin. Dyn. Syst. Ser. S (2021), 14(8): 2607-2623.
doi:10.3934/dcdss.2021032
arXiv:2009.14641.
A. Azaiez, M. Benjemaa, A. Jrajria, H. Zaag.
An explicit discontinuous Galerkin method for
blow-up solutions of nonlinear wave equations.
Turk. J. Math. (2023), 47(3):1015-1038.
doi:10.55730/1300-0098.3408.
arXiv:2008.02659.
G. Nadin, E. Ogier-Denis, A. Toledo, H. Zaag.
A Turing mechanism in order to explain the
patchy nature of Crohn's disease.
J. Math. Biol. 12 (2021).
doi:10.1007/s00285-021-01635-w.
arXiv:2007.13587.
I. Morilla, T. Léger, A. Marah, I. Pic, H. Zaag, E. Ogier-Denis.
Singular manifolds of proteomic drivers to model
the evolution of inflammatory bowel disease status.
Sci Rep 10, 19066 (2020). doi:10.1038/s41598-020-76011-7.
bioRxiv 751289.
G.K. Duong, N. Nouaili and H. Zaag.
Construction of blow-up solutions for the
Complex Ginzburg-Landau equation with critical parameters. Mem. Amer. Math. Soc., 285 (2023), no. 1411.
doi:10.1090/memo/1411. arXiv:1912.05922.
B. Abdelhedi and H. Zaag.
Construction of a blow-up solution for a
perturbed nonlinear heat equation with a gradient term.
J. Differential Equations 272 (2021) 1-45.
doi:10.1016/j.jde.2020.09.020. arXiv:1911.06392.
A. Azaiez and H. Zaag.
Classification of the blow-up behavior for a
semilinear wave equation with nonconstant coefficients.
Ann. Henri Poincaré 24 (2022), 1417-1437.
doi:10.1007/s00023-022-01247-0.
arXiv:1908.02081.
M.A. Hamza and H. Zaag.
The blow-up rate for a non-scaling invariant semilinear wave equations.
J. Math. Anal. Appl. 483, no. 2, 34p. (2020).
doi:10.1016/j.jmaa.2019.123652.
arXiv:1906.12059.
M.A. Hamza and H. Zaag.
Prescribing the center of mass of a
multi-soliton solution for a perturbed semilinear wave
equation.
J. Diff. Eqs 267 (2019), no. 6, 3524-3560.
doi:10.1016/j.jde.2019.04.018.
arXiv:1902.05051.
G.K. Duong and H. Zaag.
Profile of a touch-down solution to a nonlocal
MEMS model. Math. Models Methods Appl. Sci. 29 (2019),
no. 7, 1279-1348.
doi:10.1142/S0218202519500222.
arXiv:1811.11483.
T. Ghoul, V.T. Nguyen and H. Zaag.
Construction and stability of type I blowup
solutions for non-variational semilinear parabolic systems.
Proceedings of the Tunisian Mathematical Society Conference,
Tabarka, Tunisia, 2018.
Adv. Pure Appl. Math. 10, no. 4, 299-312 (2019).
doi:10.1515/apam-2018-0168.
arXiv:1808.05211.
T. Ghoul, V.T. Nguyen and H. Zaag.
Construction of type I blowup solutions for a
higher order semilinear parabolic equation.
Adv. Nonlinear Anal., 2020, 9, 388-412.
doi:10.1515/anona-2020-0006.
arXiv:1805.06616.
M. Ben Ayed, M.A. Jendoubi, Y. Rebai, H. Riahi and H.,
Zaag, (Eds.) (2019). Partial Differential Equations Arising
from Physics and Geometry (London Mathematical Society
Lecture Note Series). Cambridge: Cambridge University Press.
on the site of CUP.
I. Morilla, M. Uzzan, D. Cazals-Hatem,
H. Zaag, E. Ogier-Denis, G. Wainrib, X. Tréton. Topological Modelling of Deep Ulcerations
in Patients with Ulcerative Colitis.
J. Appl. Math. Phys.
5 (2017), 2244-2261.
doi:10.4236/jamp.2017.511183.
T. Ghoul, V.T. Nguyen and H. Zaag.
Blowup solutions for a reaction-diffusion system with exponential
nonlinearities. J. Diff. Eqs., 264 (2018), 7523-7579.
doi:10.1016/j.jde.2018.02.022,
arXiv:1707.08447.
F. Merle and H. Zaag.
Solution to the semilinear wave equation with a pyramid-shaped blow-up surface.
Séminaire Laurent Schwartz - EDP et applications,
(2016-2017), Exp. No. 6, 13p.r
doi:10.5802/slsedp.104.
G.K. Duong, V.T. Nguyen and H. Zaag.
Construction of a stable blowup solution with a prescribed behavior
for a non-scaling invariant semilinear heat equation.
Tunisian J. Math. 1 (2019), no. 1, pp 13--45. available on the
site of TJM.
doi:10.2140/tunis.2019.1.13.
arXiv:1704.08580.
N. Nouaili and H. Zaag. Construction of a blow-up solution for the Complex Ginzburg-Landau
equation in some critical case. Arch. Rat. Mech. Anal. 228 (2018), no. 3, 995-1058.
arXiv:1703.00081.
read-only pdf.
doi:10.1007/s00205-017-1211-3.
A. Azaiez and H. Zaag. A modulation technique for the blow-up profile of the vector-valued semilinear wave equation. Bull. Sci. Math. 141 (2017), no. 4, 312-352.
doi:10.1016/j.bulsci.2017.04.001.
arXiv:1612.05427.
T. Ghoul, V.T. Nguyen and H. Zaag.
Blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term. J. Diff. Eqs. 263 (2017), no. 8, 4517-4564.
doi:10.1016/j.jde.2017.05.023.
arXiv:1611.02474.
T. Ghoul, V.T. Nguyen and H. Zaag. Construction and stability of blowup solutions for a
non-variational semilinear parabolic system.
Ann. I. H. Poincaré
AN., 35 (2018), no. 6, 1577-1630.
doi:10.1016/j.anihpc.2018.01.003,
arXiv:1610.09883.
T. Ghoul, V.T. Nguyen and H. Zaag. Refined regularity of the blow-up set linked to refined asymptotic behavior for the semilinear heat equation. Adv. Nonlinear Stud., 17 (2017), no.1, 31-54.
doi:10.1515/ans-2016-6005. arXiv:1610.05722.
F. Merle and H. Zaag.
Blow-up solutions to the semilinear wave equation with a stylized
pyramid as a blow-up surface. Comm. Pure Appl. Math.
71, (2018), no. 9, 1850-1937.
doi:10.1002/cpa.21756 arXiv:1610.05637.
A. Azaiez, N. Masmoudi and H. Zaag.
Blow-up rate for a semilinear wave equation with exponential
nonlinearity in one space dimension.
Ben Ayed, Mohamed (ed.) et al., Partial differential equations arising
from physic and geometry. A volume in memory of Abbas Bahri. Based on
the conference, Hammamet, Tunisia, March 20-29, 2015.
Cambridge, Cambridge University Press. Lond. Math. Soc. Lect. Note
Ser. 450, 1-32 (2019).
arXiv:1601.04007.
S. Tayachi and H. Zaag.
Existence and stability of a blow-up solution with a new
prescribed behavior for a heat equation with a critical
nonlinear gradient term. Actes du Colloque EDP-Normandie, Le Havre, 21-22 octobre 2015. arXiv:1610.01289.
V.T. Nguyen and H. Zaag. Finite
degrees of freedom for the refined blow-up profile of the semilinear
heat
equation. Ann. Scient. Éc. Norm. Supér (4).
50:5 (2017), 1241-1282.
on the journal's site.
arXiv:1509.03520.
S. Tayachi and H. Zaag.
Existence of a stable blow-up profile for the nonlinear heat equation
with a critical power nonlinear gradient
term. Trans. Amer. Math. Soc., 371 (2019), 5899-5972.
doi:10.1090/tran/7631.
arXiv:1506.08306.
F. Mahmoudi, N. Nouaili and H. Zaag.
Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile. Nonlinear Anal. 131 (2016), 300-324.
doi:10.1016/j.na.2015.09.002.
arXiv:1506.07708.
V.T. Nguyen and H. Zaag. Blow-up results for a strongly perturbed semilinear heat equation: Theoretical analysis and numerical method. Anal. PDE 9 (2016), no. 1, 229-257. doi:10.2140/apde.2016.9.229.
arXiv:1410.4079.
V.T. Nguyen and H. Zaag. Construction of a stable blow-up solution for a class of strongly perturbed semilinear heat equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2016), no. 4, 1275-1314.
doi:10.2422/2036-2145.201412_001.
arXiv:1406.5233.
F. Merle and H. Zaag. On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Comm. Math. Phys. 333 (2015), no. 3, 1529-1562.
doi:10.1007/s00220-014-2132-8.
arXiv:1309.7760.
F. Merle and H. Zaag. Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Trans. Amer. Math. Soc. 368 (2016), no. 1, 27-87.
doi:10.1090/tran/6450.
arXiv:1309.7756.
Y.-P. Ding, Y. Ladeiro, Y. Bouhnik, A. Marah, H. Zaag, D. Cazals-Hatem, P. Seksik, F. Daniel, J.P. Hugot, I. Morilla, G. Wainrib, X. Tréton, and E. Ogier-Denis.
Integrative network-based analysis of colonic detoxification gene expression in Ulcerative Colitis according to smoking status. J. Crohn's Colitis
(2016), 1-11. doi:10.1093/ecco-jcc/jjw179.
N. Nouaili and H. Zaag. Profile for a simultaneously blowing up solution
for a complex valued semilinear heat equation.
Comm. Partial Differential Equations 40 (2015), 1197-1217.
doi:10.1080/03605302.2015.1018997.
on arxiv.org.
M.A. Hamza and H. Zaag. Blow-up results for semilinear wave equations in the
super-conformal case. Discrete Contin. Dyn. Syst. Ser. B,
18 (2013), no. 9, 2315-2329. doi:10.3934/dcdsb.2013.18.2315. on arxiv.org.
M.A. Hamza and H. Zaag. Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations.
Bull. Sci. Math. 137 (2013), no. 8, 1087-1109.
doi:10.1016/j.bulsci.2013.05.004,
on arxiv.org.
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., 66 (2013), no. 10, 1541-1581. doi:10.1002/cpa.21452.
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.
doi:10.1007/BF03322590.
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. 161 (2012), no. 15, 2837-2908. on arxiv.org., on the website of project Euclid.
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. Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations in the critical case. J. Hyperbolic Differ. Equ. 9 (2012), 195-221. doi: 10.1142/S0219891612500063, 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. 134 (2012), no. 3, 581-648. doi:10.1353/ajm.2012.0021 . on arxiv.org.
M.A. Hamza and H. Zaag. A Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations. Nonlinearity 25 (2012), 2759-2773. doi:10.1088/0951-7715/25/9/2759. 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,
doi:10.1090/S0002-9947-10-04902-0.
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, doi:10.1016/j.jfa.2007.03.007.
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.
on Jstor.
local 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.
doi:10.1016/j.jde.2019.04.018.
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.
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