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Determination of the blow-up rate for the semilinear wave equation

Franck Merle , Zaag Hatem
American Journal of Mathematics, 2003, 125no. 5, pp.1147--1164
Article dans une revue hal-00096450v1

Existence and universality of the blow-up profile for the semilinear wave equation in the one space dimension

Franck Merle , Hatem Zaag
Journal of Functional Analysis, 2007, A paraître
Article dans une revue hal-00166034v1

Refined Regularity of the Blow-Up Set Linked to Refined Asymptotic Behavior for the Semilinear Heat Equation

Tej-Eddine Ghoul , van Tien Nguyen , Hatem Zaag
Advanced Nonlinear Studies, 2017, 17 (1), ⟨10.1515/ans-2016-6005⟩
Article dans une revue hal-02325052v1

Detection of ulcerative colitis lesions from weakly annotated colonoscopy videos using bounding boxes

Safaa Al-Ali , John Chaussard , Sébastien Li-Thiao-Té , Éric Ogier-Denis , Alice Percy-Du-Sert , et al.
2023
Pré-publication, Document de travail hal-04308478v1

Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions

L. Corrias , Benoît Perthame , Hatem Zaag
Milan Journal of Mathematics, 2004, 72 (1), pp.1-28. ⟨10.1007/s00032-003-0026-x⟩
Article dans une revue istex hal-02326115v1

Regularity of the blow-up set and singular behavior for semilinear heat equations

Hatem Zaag
Proceedings of the Third International Palestinian Conference, Aug 2000, Bethlehem, Palestinian Territories. pp.337-347, ⟨10.1142/9789812778390_0027⟩
Communication dans un congrès hal-02326159v1

Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations in the critical case

Mohamed Ali Hamza , Hatem Zaag
Journal of Hyperbolic Differential Equations, 2012, 09 (02), pp.195-221. ⟨10.1142/S0219891612500063⟩
Article dans une revue hal-03418394v1

Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension

Frank Merle , Hatem Zaag
Journal of Functional Analysis, 2007, 253 (1), pp.43-121. ⟨10.1016/j.jfa.2007.03.007⟩
Article dans une revue hal-03418430v1

Construction and stability of a blow up solution for a nonlinear heat equation with a gradient term

M. Ebde , Hatem Zaag
SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, 2011, 55 (1), pp.5-21. ⟨10.1007/BF03322590⟩
Article dans une revue hal-03418373v1

Topological Modelling of Deep Ulcerations in Patients with Ulcerative Colitis

Ian Morilla , Mathieu Uzzan , Dominique Cazals-Hatem , Hatem Zaag , Eric Ogier-Denis , et al.
Journal of Applied Mathematics and Physics, 2017, 05 (11), pp.2244-2261. ⟨10.4236/jamp.2017.511183⟩
Article dans une revue hal-02324993v1

Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters

Giao Ky Duong , Nejla Nouaili , Hatem Zaag
Memoirs of the American Mathematical Society, 2023, 285 (1411), ⟨10.1090/memo/1411⟩
Article dans une revue hal-04307478v1

Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions

Frank Merle , Hatem Zaag
Transactions of the American Mathematical Society, 2016, 368 (1), pp.27-87. ⟨10.1090/tran/6450⟩
Article dans une revue hal-02325237v1
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The blow-up rate for a non-scaling invariant semilinear wave equations in higher dimensions

Mohamed Ali Hamza , Hatem Zaag
Nonlinear Analysis: Theory, Methods and Applications, 2021, 212, pp.112445. ⟨10.1016/j.na.2021.112445⟩
Article dans une revue hal-03418338v1
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Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension.

Frank Merle , Hatem Zaag
Séminaire Équations aux dérivées partielles (Polytechnique), 2010, France. Exp. No. 11, 10 p
Communication dans un congrès hal-00570162v1

Blow-up results for a strongly perturbed semilinear heat equation: theoretical analysis and numerical method

van Tien Nguyen , Hatem Zaag
Analysis & PDE, 2016, 9 (1), pp.229-257. ⟨10.2140/apde.2016.9.229⟩
Article dans une revue hal-02325199v1

Blow-up behavior for the Klein–Gordon and other perturbed semilinear wave equations

M.A. Hamza , Hatem Zaag
Bulletin des Sciences Mathématiques, 2013, 137 (8), pp.1087-1109. ⟨10.1016/j.bulsci.2013.05.004⟩
Article dans une revue hal-02325318v1

Unsupervised physics-informed neural network in reaction-diffusion biology models (Ulcerative colitis and Crohn's disease cases) A preliminary study

Ahmed Rebai , Louay Boukhris , Radhi Toujani , Ahmed Gueddiche , Fayad Ali Banna , et al.
2023
Pré-publication, Document de travail hal-04307465v1

Blow-up results for vector-valued nonlinear heat equations with no gradient structure

Hatem Zaag
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1998, 15 (5), pp.581-622. ⟨10.1016/S0294-1449(98)80002-4⟩
Article dans une revue hal-02326373v1

Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation

Hatem Zaag
Duke Mathematical Journal, 2006, 133 (3), pp.499-525. ⟨10.1215/S0012-7094-06-13333-1⟩
Article dans une revue istex hal-02325784v1

On the regularity of the blow-up set for semilinear heat equations

Hatem Zaag
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2002, 19 (5), pp.505-542. ⟨10.1016/S0294-1449(01)00088-9⟩
Article dans une revue hal-02326175v1
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Construction of a blow-up solution for the Complex Ginzburg-Landau equation in some critical case

Nejla Nouaili , Hatem Zaag
Archive for Rational Mechanics and Analysis, 2018, Arch. Ration. Mech. Anal., 228 (3), pp.995-1058
Article dans une revue hal-01490862v1

Modulation theory for the flat blowup solutions of nonlinear heat equation

Giao Ky Duong , Nejla Nouaili , Hatem Zaag
Communications on Pure and Applied Analysis, 2023, 22 (10), pp.2925-2959. ⟨10.3934/cpaa.2023094⟩
Article dans une revue hal-03873065v1

Integrative Network-based Analysis of Colonic Detoxification Gene Expression in Ulcerative Colitis According to Smoking Status

Yong-Ping Ding , Yannick Ladeiro , Ian Morilla , Yoram Bouhnik , Assiya Marah , et al.
Journal of Crohn's and Colitis, 2016, pp.jjw179. ⟨10.1093/ecco-jcc/jjw179⟩
Article dans une revue hal-02325288v1

Construction of a blow-up solution for a perturbed nonlinear heat equation with a gradient term

Bouthaina Abdelhedi , Hatem Zaag
Journal of Differential Equations, 2021, 272, pp.1-45. ⟨10.1016/j.jde.2020.09.020⟩
Article dans une revue hal-02370323v1

An explicit discontinuous Galerkin method for blow-up solutions of nonlinear wave equations

Asma Azaiez , Mondher Benjemaa , Aida Jrajria , Hatem Zaag
Turkish Journal of Mathematics, 2023, 47 (3), pp.1015-1038. ⟨10.55730/1300-0098.3408⟩
Article dans une revue hal-03090639v1

The blow-up rate for a non-scaling invariant semilinear wave equations

Mohamed Ali Hamza , Hatem Zaag
Journal of Mathematical Analysis and Applications, 2020, 483 (2), pp.123652. ⟨10.1016/j.jmaa.2019.123652⟩
Article dans une revue hal-02356801v1

Automatic detection of bleeding and ulcers in endoscopic videos for ulcerative colitis

Safaa Al-Ali , John Chaussard , Sébastien Li-Thiao-Té , Hatem Zaag
2021
Pré-publication, Document de travail hal-03418329v1

Stability of the blow-up profile for equations of the type $u_t=\Delta u+|u|^{p-1}u$

Frank Merle , Hatem Zaag
Duke Mathematical Journal, 1997, 86 (1), pp.143-195. ⟨10.1215/S0012-7094-97-08605-1⟩
Article dans une revue istex hal-02326383v1
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Stabilité du profil à l'explosion pour les équations du type $u\sb t=\Delta u+\vert u\vert \sp {p-1}u$.

Frank Merle , Hatem Zaag
Comptes rendus de l'Académie des sciences. Série I, Mathématique, 1996
Article dans une revue hal-02326423v1

A modulation technique for the blow-up profile of the vector-valued semilinear wave equation

Asma Azaiez , Hatem Zaag
Bulletin des Sciences Mathématiques, 2017, 141 (4), pp.312-352. ⟨10.1016/j.bulsci.2017.04.001⟩
Article dans une revue hal-02325035v1