NB: Pour certains articles de la liste ci-dessous, quelques corrections (mineures) sont indiquées; prière d'ouvrir les fichiers ''Erratum'' correspondants.
LIVRE
[A] Superlinear parabolic problems. Blow-up, global existence and steady states (avec Pavol Quittner) Birkhauser Advanced Texts, 2007, 584 p.+xi. ISBN: 978-3-7643-8441-8 Détails Mises à jour et errata
1 - Articles soumis
[68] Transversality of stable and Nehari manifolds for a semilinear heat equation (avec Flavio Dickstein, Noriko Mizoguchi et Fred Weissler), soumis
2 - Articles parus ou acceptés dans des revues avec comité de lecture
[67] The influence of space dimension on the large-time behavior in a reaction-diffusion system modeling diallelic selection (avec Michael Winkler), J. Math. Biology, accepté
[66] Non-selfsimilar dead-core rate for the fast diffusion equation with strong absorption (avec Jong-Shenq Guo et Chia-Tung Ling), Nonlinearity, 23 (2010) 657-673
[65] Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains (avec Yuxiang Li), Comm. Math. Phys., 293 (2010), 499-517
[64] Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source (avec Kaouther Ammar), Discrete Contin. Dynam. Systems, 26 (2010), 665-689
[63] The proof of the Lane-Emden conjecture in four space dimensions, Advances in Mathematics, 221 (2009), 1409-1427
[62] An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source, J. Differential Equations, 246 (2009), 3980-4005
[61] Single-point blow-up for a semilinear parabolic system, J. Eur. Math. Soc., 11 (2009), 169-188
[60] Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk (avec Nikos Kavallaris), SIAM J. Math. Analysis, 41 (2008/9), 128-157
[59] Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part II: Parabolic equations (avec Peter Polacik et Pavol Quittner), Indiana Univ. Math. J., 56 (2007), 879-908
[58] Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part I: Elliptic equations and systems (avec Peter Polacik et Pavol Quittner), Duke Math. J., 139 (2007), 555-579
[57] A note on diffusion-induced blow-up, J. Dynamics Differ. Equations, 19 (2007) 819-823
[56] A remark on the large-time behavior of solutions of viscous Hamilton-Jacobi equations, Acta Math. Univ. Comenian., 76 (2007), 11-13
[55] Global solutions of inhomogeneous Hamilton-Jacobi equations (avec Qi S. Zhang), J. d'Analyse Math., 99 (2006), 355-396
[54] Sharp gradient estimate and Yau's Liouville theorem for the heat equation on noncompact manifolds (avec Qi S. Zhang), Bull. London Math. Soc., 38 (2006), 1045-1053
[53] Stabilization towards a singular steady state with gradient blow-up for a convection-diffusion problem (avec Juan Luis Vazquez), Discrete Contin. Dynam. Systems, 14 (2006), 221-234
[52] Optimal growth rates for a viscous Hamilton-Jacobi equation (avec Philippe Laurencot) J. Evolution Equations, 5 (2005), 123-135
[51] Optimal regularity conditions for elliptic problems via $L^p_delta$ spaces, Duke Math. J., 127 (2005), 175-192
[50] Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up (avec Jong-Shenq Guo) Mathematische Annalen, 331 (2005), 651-667 Erratum
[49] Coexistence of simultaneous and non-simultaneous blow-up in a semilinear parabolic system (avec Julio Rossi), Differential Integral Equations, 18 (2005), 405-418
[48] Infinite time blow-up for superlinear parabolic problems with localized reaction, Proc. Amer. Math. Soc., 133 (2005), 431-436
[47] A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces (avec Pavol Quittner), Archive Rational Mech. Anal., 174 (2004), 49-81
[46] Gradient bounds for solutions of semilinear parabolic equations without Bernstein's quadratic condition (avec Jean-Philippe Bartier), C. R. Acad. Sc. Paris, 338 (2004), 533-538
[45] Uniform blow-up profile and boundary behavior for a nonlocal reaction-diffusion equation with critical damping, Math. Methods in the Applied Sciences, 27 (2004), 1819-1829 [Numéro spécial "Singularity Formation in Non-linear Evolution Equations", en l'honneur du 60ème anniversaire du Prof. Howard A. Levine]
[44] Instantaneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations (avec Julia Matos), Houston J. Math., 30 (2004), 879-890
[43] Optimal condition for non-simultaneous blow-up in a reaction-diffusion system (avec Slim Tayachi) J. Math. Soc. Japan, 56 (2004), 571-584
[42] Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena (avec Jose Arrieta et Anibal Rodriguez-Bernal), Annali Scuola Norm. Sup. Pisa (5), 3 (2004), 1-15
[41] Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory, Z. angewandte Math. und Phys., 55 (2004), 28-31
[40] Initial blow-up rates and universal bounds for nonlinear heat equations (avec Pavol Quittner et Michael Winkler) J. Differential Equations, 196 (2004), 316-339
[39] An example of uniformly recurrent function which is not almost periodic (avec Alain Haraux), J. Fourier Analysis and Appl., 10 (2004), 217-220
[38] Universal bounds for global solutions of fast diffusion equations with source, Commun. Partial Differ. Equations, 28 (2003), 2029-2044
[37] Bounds of global solutions of parabolic problems with nonlinear boundary conditions (avec Pavol Quittner) Indiana Univ. Math. J., 52 (2003), 875-900
[36] Universal blow-up rates for a semilinear heat equation and applications (avec Julia Matos), Advances Differ. Equations, 8 (2003), 615-639
[35] A priori estimates of global solutions of superlinear parabolic problems without variational structure (avec Pavol Quittner), Discrete Contin. Dynam. Systems, 9 (2003), 1277-1292
[34] On the growth of mass for a viscous Hamilton-Jacobi equation (avec Philippe Laurencot) J. d'Analyse Math., 89 (2003), 367-383
[33] Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state (avec Fred Weissler), Ann. Inst. H. Poincaré, Analyse non linéaire, 20 (2003), 213-235
[32] Oscillatory blowup in nonlinear second order ODEs: the critical case (avec Mikhael Balabane et Mustapha Jazar) Discrete Contin. Dynam. Systems, 9 (2003), 577-584
[31] A priori and universal estimates for global solutions of superlinear degenerate parabolic equations, Annali Mat. Pura Appl., 181 (2002), 427-436
[30] Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations, Portugaliae Math., 59 (2002), 315-324
[29] Extinction and non-extinction for viscous Hamilton-Jacobi equations in R^N (avec Said Benachour, Philippe Laurencot et Didier Schmitt) Asymptotic Analysis, 31 (2002) 229-246
[28] Stability for semilinear parabolic equations with decaying potentials in R^n and dynamical approach to the existence of ground states (avec Qi S. Zhang), Ann. Inst. H. Poincaré, Analyse non linéaire, 19 (2002), 683-703
[27] Global existence from single-component $L_p$ estimates in a semilinear reaction-diffusion system (avec Pavol Quittner), Proc. Amer. Math. Soc., 130 (2002), 2719-2724
[26] The local theory for viscous Hamilton-Jacobi equations in Lebesgue spaces (avec Matania Ben-Artzi et Fred Weissler), J. Math. Pures et Appliquées, 81 (2002) 343-378
[25] Critical blowup exponents for a system of reaction-diffusion equations with absorption (avec Nabil Bedjaoui), Z. angewandte Math. und Phys., 53 (2002), 197-210
[24] Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions, Differential Integral Equations, 15 (2002), 237-256
[23] The blow-up rate for semilinear parabolic problems on general domains (avec Marek Fila), Nonlinear Differ. Eq. and Applications NoDEA, 8 (2001), 473-480
[22] Admissible $L_p$ norms for local existence and for continuation in parabolic systems are not the same (avec Pavol Quittner), Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 1435-1456
[21] Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem (avec Marek Fila), Interfaces and Free Boundaries, 3 (2001), 337-344
[20] Linear and nonlinear heat equations in $L^q_delta$ spaces and universal bounds for global solutions (avec Marek Fila et Fred Weissler), Mathematische Annalen, 320 (2001), 87-113
[19] Blow-up rates for nonlinear heat equations with gradient terms and for parabolic inequalities (avec Slim Tayachi), Colloquium Mathematicum, 88 (2001), 135-154
[18] Decay of global solutions, stability and blow-up for a reaction-diffusion problem with free boundary (avec Hamid Ghidouche et Domingo Tarzia), Proc. Amer. Math. Soc., 129 (2001), 781-792
[17] Small time boundary behavior for parabolic equations with noncompatible data (avec Yvan Martel), J. Math. Pures et Appliquées, 79 (2000), 603-632
[16] Decay of heat semigroups in L$^infty$ and applications to nonlinear parabolic problems in unbounded domains, J. Functional Analysis, 173 (2000), 343-360
[15] A note on the paper by Qi S. Zhang: "A priori estimates and the representation formula for all positive solutions to a semilinear parabolic problem", J. Math. Analysis and Applications, 243 (2000), 453-457
[14] Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations, Commun. Partial Differ. Equations, 24 (1999), 951-973
[13] Poincaré's inequality and global solutions of a nonlinear parabolic equation (avec Fred Weissler), Ann. Inst. H. Poincaré, Analyse non linéaire, 16 (1999), 337-373
[12] Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source, J. Differential Equations, 153 (1999), 374-406 Erratum
[11] Sharp stability estimates for quasi-autonomous evolution equations of hyperbolic type, Quarterly of Applied Math., 57 (1999), 55-85
[10] Blow-up in nonlocal reaction-diffusion equations, SIAM J. Math. Analysis, 29 (1998), 1301-1334
[9] Critical exponents, special large-time behavior and oscillatory blow-up in nonlinear ODE's, Differential Integral Equations, 11 (1998), 147-167
[8] Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations, Nonlinear Analysis, 32 (1998), 279-286
[7] Self-similar subsolutions and blow-up for nonlinear parabolic equations (avec Fred Weissler), J. Math. Analysis and Applications, 212 (1997), 60-74
[6] Sur l'asymptotique des solutions globales pour une équation de la chaleur semi-linéaire dans des domaines non bornés, C. R. Acad. Sc. Paris, 323, Série I (1996), 877-882 Erratum
[5] Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term (avec Slim Tayachi et Fred Weissler), Indiana Univ. Math. J., 45 (1996), 655-682
[4] Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications, Math. Methods in the Applied Sciences, 19 (1996), 1317-1333
[3] Uniqueness and non-uniqueness results for the antiperiodic solutions of some nonlinear second-order evolution equations, Nonlinear Analysis, 26 (1996), 1511-1525
[2] Nonexistence of global solutions to some differential inequalities of the second order and applications, Portugaliae Mathematica, 52 (1995), 289-299
[1] Existence of exceptional growing-up solutions for a class of nonlinear second order ordinary differential equations, Asymptotic Analysis, 11 (1995), 185-207
3 - Articles de synthèse
[72] The influence of gradient perturbations on blow-up asymptotics in semilinear parabolic problems: a survey, Proceedings of the conference in honor of H. Amann (Zuerich 2004), Progress in Nonlinear Differential Equations and Their Applications, Vol. 64, Birkhaueser, pp. 473-496
[71] A survey on $L^p_delta$ spaces and their applications to nonlinear elliptic and parabolic problems, Proceedings of the international conference Nonlinear Partial Differential Equations and Their Applications, Fudan Univ., Shanghai 2003. Gakuto International Series, Math. Sc. and Appl., 20 (2004), 464-479.
[70] Recent results and open problems on parabolic equations with gradient nonlinearities, Electronic J. Differ. Equations, Vol. 2001 (2001), No. 20, pp. 1-19.
[69] Blow-up behavior in nonlocal vs local heat equations, Proceedings of the minisemester on evolution equation, Polish Academy of Sciences, Inst. of Mathematics (Warsaw, Sept 1998) Banach Center Publ., 52 (2000), 221-226
4 - Notes aux C.R.A.S. préliminaires
[78] Existence of ground states for semilinear elliptic equations with decaying mass: a parabolic approach (avec Qi S. Zhang), C. R. Acad. Sc. Paris, 332, Série I (2001), 515-520
[77] Sur la non-existence et la non-unicité des solutions du problème de Cauchy pour une équation parabolique semi-linéaire (avec Matania Ben-Artzi et Fred Weissler), C. R. Acad. Sc. Paris, 329, Série I (1999), 371-376
[76] Estimations optimales en temps petit et près de la frontière pour les solutions de l'équation de la chaleur avec données non-compatibles (avec Yvan Martel), C. R. Acad. Sc. Paris, 327, Série I (1998), 575-580
[75] Résultats d'explosion en temps fini pour une équation de la chaleur non linéaire, C. R. Acad. Sc. Paris, 321, Série I (1995), 721-726
[74] Une condition optimale d'unicité pour les solutions antipériodiques d'équations d'évolution paraboliques, C. R. Acad. Sc. Paris, 319, Série I (1994), 1037-1041
[73] Etude des solutions globales de certaines équations différentielles ordinaires du second ordre non linéaires, C. R. Acad. Sc. Paris, 313, Série I (1991), 365-370
5 - Actes de congrès
[82] Universal estimates for the blow-up rate in a semilinear heat equation (avec Julia Matos) in: Proceedings of the 4th European Conference on Elliptic and Parabolic Problems (Rolduc, June 2001), pp. 165-174, World Scientific, 2002
[81] Some blow-up results for nonlocal reaction-diffusion equations, in: Proceedings of the 3rd European Conference on Elliptic and Parabolic Problems (Pont-à-Mousson, June 1997), pp. 127-137, Pitman Research Notes in Mathematics Series, #384, Addison Wesley Longman, 1998
[80] Self-similar subsolutions and blow-up for nonlinear parabolic equations (avec Fred Weissler), Nonlinear Analysis, Proc. of the 2nd World Congress of Nonlinear Analysis (Athens, July 1996), 30 (1997), 4637-4641
[79] Unicité et non-unicité des solutions antipériodiques pour certaines équations d'évolution non linéaires du second ordre, in: Actes du 25ème Congrès National d'Analyse Numérique (Giens, mai 1993), pp. 225-226, Université de Franche-Comté, 1993
6 - Thèses
[84] Contribution à l'étude des équations paraboliques non linéaires et de quelques autres équations d'évolution, Mémoire d'Habilitation à diriger des recherches, Université Paris-Nord, janvier 1998
[83] Propriétés globales de quelques équations d'évolution non linéaires du second ordre, Thèse de Doctorat de l'Université Paris 6, janvier 1994
7 - Divers (épistémologie, enseignement)
[86] Introduction à l'Analyse numérique, in: Actes du Colloque "Math en Jeans", pp. 105-120, 1995
[85] Un apercu du problème du déterminisme scientifique, Cahiers du CREA, 14 (1990), 347-383