PUBLICATIONS of Philippe Souplet

NB: For some items in the list below, a few (minor) corrections are given; please open the corresponding ''Erratum'' files.

BOOK

[A] Superlinear parabolic problems. Blow-up, global existence and steady states (with Pavol Quittner)
Birkhauser Advanced Texts, 2007, 584 p.+xi. ISBN: 978-3-7643-8441-8
Details
Updates and errata

1 - Submitted papers

[89] Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity (with Carlos Esteve), submitted [ArXiV]

[88] No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem (with Carlos Esteve), submitted [ArXiV]

[87] Excluding blowup at zero points of the potential by means of Liouville-type theorems (with Jong-Shenq Guo), [ArXiV]

2- Refereed papers

[86] Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation (with Alessio Porretta),
Ann. Inst. H. Poincaré, Analyse non linéaire 34 (2017), 1913-1923 [ArXiV]

[85] The profile of boundary gradient blow-up for the diffusive Hamilton-Jacobi equation (with Alessio Porretta),
International Math. Research Notices 17 (2017), 5260-5301 [ArXiV]

[84] Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in R^n,
J. Functional Analysis 272 (2017), 2005-2037 [ArXiV]

[83] Single-point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $p$-Laplacian diffusion (with Amal Attouchi),
Trans. Amer. Math. Soc. 369 (2017), 935-974 [ArXiV]

[82] A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems (with Quoc Hung Phan),
Math. Annalen 366 (2016), 1561-15 [ArXiV]

[81] Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities (with Slim Tayachi),
Nonlinear Analysis 138 (2016) 428-447 [Special issue in honor of Juan Luis Vázquez' 70th birthday] [ArXiV]

[80] Improved conditions for single-point blow-up in reaction-diffusion systems (with Nejib Mahmoudi and Slim Tayachi),
J. Differential Equations 259 (2015), 1898-1932 [ArXiV]

[79] A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient,
Nonlinear Analysis 121 (2015), 412-423 [Special issue in honor of Enzo Mitidieri's 60th birthday] [ArXiV]

[78] No touchdown at zero points of the permittivity profile for the MEMS problem (with Jong-Shenq Guo),
SIAM J. Math. Analysis 47 (2015), 614-625 [ArXiV]

[77] Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems (with Alexandre Montaru and Boyan Sirakov),
Archive Rational Mech. Anal. 213 (2014), 129-169 [ArXiV]

[76] Nondegeneracy of blow-up points for the parabolic Keller-Segel System (with Noriko Mizoguchi),
Ann. Inst. H. Poincaré, Analyse non linéaire 31 (2014), 851-875

[75] Global existence of solutions for a chemotaxis-type system arising in crime modeling (with Raul Manasevich and Quoc Hung Phan),
Europ. J. Appl. Math. 24 (2013), 273-296 [ArXiV]

[74] Liouville-type theorems for elliptic Schr\"odinger systems associated with copositive matrices,
Netw. Heterog. Media, 7 (2012), 967-988 [Special issue in honor of Hiroshi Matano's 60th birthday]

[73] Symmetry of components for semilinear elliptic systems (with Pavol Quittner),
SIAM J. Math. Analysis 44 (2012), 2545-2559

[72] Classification of large-time behaviors in a reaction-diffusion system modeling diallelic selection (with Michael Winkler),
Math. Biosciences 239 (2012) 191-206

[71] Optimal Liouville-type theorems for noncooperative elliptic Schr\"odinger systems and applications (with Pavol Quittner),
Comm. Math. Phys. 311 (2012), 1-19

[70] Liouville-type theorems and bounds of solutions of Hardy-Hénon equations (with Quoc Hung Phan),
J. Differential Equations 252 (2012), 2544-2562

[69] Blow-up rate of solutions of parabolic problems with nonlinear boundary conditions (with Pavol Quittner),
Discrete Contin. Dynam. Systems, Series S 5 (2012), 671-681

[68] Transversality of stable and Nehari manifolds for a semilinear heat equation (with Flavio Dickstein, Noriko Mizoguchi and Fred Weissler),
Calculus of Variations and PDE 42 (2011), 547-562

[67] The influence of space dimension on the large-time behavior in a reaction-diffusion system modeling diallelic selection (with Michael Winkler),
J. Math. Biology, 62 (2011), 391-421

[66] Non-selfsimilar dead-core rate for the fast diffusion equation with strong absorption (with Jong-Shenq Guo and Chia-Tung Ling),
Nonlinearity, 23 (2010) 657-673
Erratum

[65] Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains (with Yuxiang Li),
Comm. Math. Phys., 293 (2010), 499-517

[64] Liouville-type theorems and universal bounds for positive solutions of the porous medium equation with source (with Kaouther Ammar),
Discrete Contin. Dynam. Systems, Series A, 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 (with Nikos Kavallaris),
SIAM J. Math. Analysis, 41 (2008/9), 128-157
Erratum [ArXiV]

[59] Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part II: Parabolic equations (with Peter Polacik and 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 (with Peter Polacik and 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 (with 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 (with Qi S. Zhang),
Bull. London Math. Soc., 38 (2006), 1045-1053 [ArXiV]

[53] Stabilization towards a singular steady state with gradient blow-up for a convection-diffusion problem (with Juan Luis Vázquez),
Discrete Contin. Dynam. Systems, Series A, 14 (2006), 221-234

[52] Optimal growth rates for a viscous Hamilton-Jacobi equation (with 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 (with Jong-Shenq Guo)
Mathematische Annalen, 331 (2005), 651-667
Erratum

[49] Coexistence of simultaneous and non-simultaneous blow-up in a semilinear parabolic system (with 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 (with Pavol Quittner),
Archive Rational Mech. Anal., 174 (2004), 49-81

[46] Gradient bounds for solutions of semilinear parabolic equations without Bernstein's quadratic condition (with 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 [Special issue "Singularity Formation in Non-linear Evolution Equations", in honor of Howard A. Levine's 60th birthday]

[44] Instantaneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations (with Julia Matos),
Houston J. Math., 30 (2004), 879-890

[43] Optimal condition for non-simultaneous blow-up in a reaction-diffusion system (with Slim Tayachi)
J. Math. Soc. Japan, 56 (2004), 571-584

[42] Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena (with Jose Arrieta and 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 (with Pavol Quittner and Michael Winkler)
J. Differential Equations, 196 (2004), 316-339

[39] An example of uniformly recurrent function which is not almost periodic (with 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 (with Pavol Quittner),
Indiana Univ. Math. J., 52 (2003), 875-900

[36] Universal blow-up rates for a semilinear heat equation and applications (with Julia Matos),
Advances Differ. Equations, 8 (2003), 615-639

[35] A priori estimates of global solutions of superlinear parabolic problems without variational structure (with Pavol Quittner),
Discrete Contin. Dynam. Systems, Series A, 9 (2003), 1277-1292

[34] On the growth of mass for a viscous Hamilton-Jacobi equation (with 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 (with Fred Weissler),
Ann. Inst. H. Poincaré, Analyse non linéaire, 20 (2003), 213-235

[32] Oscillatory blowup in nonlinear second order ODEs: the critical case (with Mikhael Balabane and Mustapha Jazar)
Discrete Contin. Dynam. Systems, Series A, 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 (with Said Benachour, Philippe Laurencot and 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 (with 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 (with Pavol Quittner),
Proc. Amer. Math. Soc., 130 (2002), 2719-2724

[26] The local theory for viscous Hamilton-Jacobi equations in Lebesgue spaces (with Matania Ben-Artzi and Fred Weissler),
J. Math. Pures Appl., 81 (2002), 343-378

[25] Critical blowup exponents for a system of reaction-diffusion equations with absorption (with 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 (with 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 (with 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 (with 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 (with Marek Fila and Fred Weissler),
Mathematische Annalen, 320 (2001), 87-113

[19] Blow-up rates for nonlinear heat equations with gradient terms and for parabolic inequalities (with 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 (with Hamid Ghidouche and Domingo Tarzia),
Proc. Amer. Math. Soc., 129 (2001), 781-792

[17] Small time boundary behavior for parabolic equations with noncompatible data (with 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 (with 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 (with 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 (with Slim Tayachi and 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 - Survey papers

[94] Parabolic Liouville-type theorems via their elliptic counterparts (avec Pavol Quittner),
Discrete Contin. Dynam. Syst., special issue 2011, pp. 1206-1213

[93] 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

[92] 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

[91] Recent results and open problems on parabolic equations with gradient nonlinearities,
Electronic J. Differ. Equations, Vol. 2001 (2001), No. 20, pp. 1-19

[90] 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 - Preliminary C.R.A.S. Notes

[101] Symmetry of components and Liouville theorems for noncooperative elliptic systems on the half-space (with Alexandre Montaru),
C. R. Acad. Sci. Paris, Ser. I 352 (2014) 321-325

[100] Existence of ground states for semilinear elliptic equations with decaying mass: a parabolic approach (with Qi S. Zhang),
C. R. Acad. Sc. Paris, 332, Série I (2001), 515-520

[99] Sur la non-existence et la non-unicité des solutions du problème de Cauchy pour une équation parabolique semi-linéaire (with M. Ben-Artzi and F. Weissler),
C. R. Acad. Sc. Paris, 329, Série I (1999), 371-376

[98] Estimations optimales en temps petit et près de la frontière pour les solutions de l'équation de la chaleur avec données non-compatibles (with Y. Martel),
C. R. Acad. Sc. Paris, 327, Série I (1998), 575-580

[97] 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

[96] 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

[95] 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 - Proceedings

[105] Universal estimates for the blow-up rate in a semilinear heat equation (with J. Matos)
in: Proceedings of the 4th European Conference on Elliptic and Parabolic Problems (Rolduc, June 2001), pp. 165-174, World Scientific, 2002

[104] 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

[103] Self-similar subsolutions and blow-up for nonlinear parabolic equations (with F. Weissler),
Nonlinear Analysis, Proc. of the 2nd World Congress of Nonlinear Analysis (Athens, July 1996), 30 (1997), 4637-4641

[102] 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 - Theses

[107] Contribution à l'étude des équations paraboliques non linéaires et de quelques autres équations d'évolution,
Mémoire d'Habilitation à diriger des recherches (Habilitation thesis), Université Paris-Nord, January 1998

[106] Propriétés globales de quelques équations d'évolution non linéaires du second ordre,
Thèse de Doctorat (PhD Thesis), Université Paris 6, January 1994

7 - Miscellaneous (epistemology, teaching)

[109] Introduction à l'Analyse numérique,
in: Actes du Colloque "Math en Jeans", pp. 105-120, 1995

[108] Un apercu du problème du déterminisme scientifique,
Cahiers du CREA, 14 (1990), 347-383