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Thierry Cazenave



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Publications

La plupart de ces articles sont disponibles en version pdf. N'hésitez pas à me les demander.

Most of these articles are available in pdf. Do not hesitate to ask me.

Cazenave T., Equations de Schrödinger non linéaires en dimension deux, Proc. Royal Soc. Edinburgh Sect. A 84 (1979), no. 3-4, 327-346. pdf

Cazenave T. and Haraux A., Equations d'évolution avec non-linéarité logarithmique, Ann. Fac. Sci. Toulouse Math. 2 (1980), no. 1, 21-51. pdf

Berestycki H. and Cazenave T., Instabilité des états stationaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 9, 489-492. pdf

Cazenave T. and Lions P.-L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys. 85 (1982), no. 4, 549-561. pdf

Cazenave T., Stable solutions of the logarithmic Schrödinger equation, Nonlinear Anal. 7 (1983), no. 10, 1127-1140. pdf

Berestycki H. and Cazenave T., Instability of stationary states in nonlinear Schrödinger and Klein-Gordon equations, Publications du Laboratoire d'Analyse Numérique 84001 (1984). pdf

Cazenave T. and Lions P.-L., Solutions globales d'équations de la chaleur semi linéaires, Comm. Partial Differential Equations 9 (1984), no. 10, 955-978. pdf

Cazenave T., Uniform estimates for solutions of nonlinear Klein-Gordon equations, J. Funct. Anal. 60 (1985), no. 1, 36-55. pdf

Cazenave T. and Vázquez L., Existence of localized solutions for a nonlinear classical Dirac field, Comm. Math. Phys. 105 (1986), no. 1, 35-47. pdf

Cazenave T. and Haraux A., Oscillatory phenomena associated to semilinear wave equations in one spatial dimension, Trans. Amer. Math. Soc. 300 (1987), no. 1, 207-233. pdf

Cazenave T. and Haraux A., Some oscillation properties of the wave equation in several space dimensions, J. Funct. Anal. 76 (1988), no. 1, 87-109. pdf

Cazenave T. and Weissler F.B., The Cauchy problem for the nonlinear Schrödinger equation in H1, Manuscripta Math. 61 (1988), no. 4, 477-494. pdf

Balabane M., Cazenave T., Douady A. and Merle F., Existence of excited states for a nonlinear Dirac field, Comm. Math. Phys. 119 (1988), no. 1, 153-176. pdf

Cazenave T. and Esteban M.J., On the stability of stationary states for nonlinear Schrödinger equations with an external magnetic field, Mat. Apl. Comput. 7 (1988), no. 3, 155-168. pdf

Cazenave T., Haraux A., Vázquez L. and Weissler F.B., Nonlinear effects in the wave equation with a cubic restoring force, Comp. Mech. 5 (1989), 49-72. pdf

Cazenave T. and Weissler F.B., Some remarks on the nonlinear Schrödinger equation in the critical case, in Nonlinear Semigroups, Partial Differential Equations, and Attractors, T.L. Gill and W.W. Zachary (eds.), Lecture Notes in Math. 1394, Springer, New York, 1989, 18-29. pdf

Cazenave T., On the existence of stationary states for classical nonlinear Dirac fields, in Hyperbolic Systems and Mathematical Physics, Textos e Notas 41, C.M.A.F., Lisbonne, 1989, 61--114. pdf

Cazenave T., An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos 22, I.M.U.F.R.J., Rio de Janeiro, 1989. pdf

Cazenave T. and Weissler F.B., The Cauchy problem for the critical nonlinear Schrödinger equation in Hs, Nonlinear Anal. 14 (1990), no. 10, 807-836. pdf

Cazenave T. and Haraux A., Introduction aux problèmes d'évolution semi-linéaires , Mathématiques et Applications 1, Ellipses, Paris, 1990.

Balabane M., Cazenave T. and Vázquez L., Existence of standing waves for Dirac fields with singular nonlinearities, Comm. Math. Phys. 133 (1990), no. 1, 53-74. pdf

Cazenave T. and Weissler F.B., The structure of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation, Proc. Royal Soc. Edinburgh Sect. A 117 (1991), no. 3-4, 251-273. pdf

Cazenave T. and Weissler F.B., Rapidly decaying solutions of the nonlinear Schrödinger equation, Comm. Math. Phys. 147 (1992), no. 1, 75-100. pdf

Cazenave T., Haraux A. and Weissler F.B., A class of nonlinear completely integrable abstract wave equations, J. Dynam. Differential Equations 5 (1993), no. 1, 129-154. pdf

Cazenave T., Haraux A. and Weissler F.B., Detailed asymptotics for a convex Hamiltonian system with two degrees of freedom, J. Dynam. Differential Equations 5 (1993), no. 1, 155-187. pdf

Cazenave T. and Escobedo M., A two parameter shooting problem for a second order differential equation, J. Differential Equations 113 (1994), no. 2, 418-451. pdf

Cazenave T., Blow up and scattering in the nonlinear Schrödinger equation , Textos de Métodos Matemáticos 30, I.M.U.F.R.J., Rio de Janeiro, 1994. pdf

Cazenave T. and Weissler F.B., Asymptotically periodic solutions for a class of nonlinear coupled oscillators, Portugal. Math. 52 (1995), no. 1, 109-123. pdf

Cazenave T. and Weissler F.B., Unstable simple modes of the nonlinear string, Quart. Appl. Math. 54 (1996), no. 2, 287-305. pdf

Cazenave T. and Dickstein F., On the initial value problem for a linear model of well-reservoir coupling, Nonlinear World 3 (1996), no. 3, 567-587. pdf

Brezis H., Cazenave T., Martel Y. and Ramiandrisoa A., Blow up for ut-Δu=g(u) revisited, Adv. Differential Equations 1 (1996), no. 1, 73-90. pdf

Brezis H. and Cazenave T., A nonlinear heat equation with singular initial data, J. Anal. Math. 68 (1996), 277-304. pdf

Cazenave T., Dickstein F. and Kavian O., A parameter determination problem for a linear model of well-reservoir coupling, Mat. Contemp. 10 (1996), 87-97. pdf

Cazenave T., Shatah J. and Shadi Tahvildar Zadeh A., Harmonic maps of the Hyperbolic space and development of singularities in wave maps and Yang-Mills fields, Ann. Inst. H. Poincaré Phys. Théor. 68 (1998), no. 3, 315-349. pdf

Cazenave T. and Dickstein F., Implicit finite difference schemes for a linear model of well-reservoir coupling, IMA J. Numer. Anal. 18 (1998), no. 1, 91-120. pdf

Cazenave T. and Weissler F.B., Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z. 228 (1998), no. 1, 83-120. pdf

Cazenave T. and Haraux A., An introduction to semilinear evolution equations , Oxford Lecture Series in Mathematics and its Applications 13, Oxford University Press, Oxford, 1998.

Cazenave T. and Weissler F.B., More self-similar solutions of the nonlinear Schrödinger equation, NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 3, 355-365. pdf

Cazenave T., Dickstein F. and Escobedo M., A semilinear heat equation with concave-convex nonlinearity, Rend. Mat. Appl. (7) 19 (1999), no. 2, 211-242. pdf

Cazenave T. and Weissler F.B., Scattering theory and self-similar solutions for the nonlinear Schrödinger equation, SIAM J. Math. Anal. 31 (2000), no. 3, 625-650. pdf

Cazenave T. and Dickstein F., On the influence of boundary conditions on flows in porous media, J. Math. Anal. Appl. 253 (2001), no. 1, 79-106. pdf

Cazenave T., Vega L. and Vilela M.C., A note on the nonlinear Schrödinger equation in weak Lp spaces, Commun. Contemp. Math. 3 (2001), no. 1, 153-162. pdf

Cazenave T., Dickstein F., Escobedo M. and Weissler F.B., Self-similar solutions of a nonlinear heat equation, J. Math. Sci. Univ. Tokyo 8 (2001), no. 3, 501-540. pdf

Cazenave T., Escobedo M. and Pozio M.A., Some stability properties for minimal solutions of -Δu=λg(u), Portugal. Math . 59 (2002), no. 4, 373-391. pdf

Cazenave T., Dickstein F. and Weissler F.B., Universal solutions of the heat equation, Discrete Cont. Dyn. Systems 9 (2003), no. 5, 1105-1132. pdf

Cazenave T., Dickstein F. and Weissler F.B., Universal solutions of a nonlinear heat equation, Ann. Scuola Norm. Sup. Pisa, Cl. Sci (5) 2 (2003), no. 1, 77-117. pdf

Cazenave T., Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003. 323 pp. ISBN: 0-8218-3399-5.

Cazenave T., Dickstein F. and Weissler F.B., Chaotic behavior of solutions of the Navier-Stokes system in RN, Adv. Differential Equations 10 (2005), no. 4, 361-398. pdf

Cazenave T., Dickstein F. and Weissler F.B., A solution of the heat equation with a continuum of decay rates, in Elliptic and parabolic problems: A special tribute to the work of Haïm Brezis, Progress in Nonlinear Differential Equations and their Applications 63. Birkhäuser Verlag, Basel, 2005, 135-138. pdf

Cazenave T., Dickstein F. and Weissler F.B., Multiscale asymptotic behavior of a solution of the heat equation in RN, in Contributions to nonlinear analysis. A tribute to D. G. de Figueiredo on the occasion of his 70th birthday , Progress in Nonlinear Differential Equations and their Applications 66. Birkhäuser Verlag, Basel, 2005, 185-194. pdf

Cazenave T., Dickstein F. and Weissler F.B., A solution of the constant coefficient heat equation in R with exceptional asymptotic behavior: an explicit construction, J. Math. Pures Appl. 85 (2006), no. 1, 119-150. pdf

Cazenave T. and Weissler F.B., Spatial decay and time-asymptotic profiles for solutions of Schrödinger equations, Indiana Univ. Math. J.   55 (2006), no. 1, 75-118. pdf

Cazenave T., An introduction to semilinear elliptic equations, Editora do IM-UFRJ, Rio de Janeiro, 2006. ix+193 pp. ISBN: 85-87674-13-7. 2nd Ed. 2018, ISBN: 978-85-87674-31-9. pdf

Cazenave T., Dickstein F. and Weissler F.B., Nonparabolic asymptotic limits of solutions of the heat equation on RN, J. Dynam. Differential Equations 19, (2007), no. 3, 789-818. pdf

Cazenave T., Dickstein F. and Weissler F.B., An equation whose Fujita critical exponent is not given by scaling, Nonlinear Anal. 68, (2008), no. 4, 862-874. pdf

Cazenave T., Dickstein F. and Weissler F.B., Global existence and blowup for sign-changing solutions of the nonlinear heat equation, J. Differential Equations 344 (2009), no. 7, 2669-2680. pdf

Cazenave T., Dickstein F. and Weissler F.B., Sign-changing stationary solutions and blowup for the nonlinear heat equation in a ball, Math. Ann 246 (2009), no. 2, 431-449. pdf

Cazenave T., Dickstein F. and Weissler F.B., On the structure of global solutions of the nonlinear heat equation in a ball, J. Math. Anal. Appl. 360 (2009), no. 2, 537-547. pdf

Xie J., Zhang L. and Cazenave T., A note on decay rates for Schrödinger's equation, Proc. Amer. Math. Soc. 138 (2010), no. 1, 199-207. pdf

Cazenave T. and Scialom M., A Schrödinger equation with time-oscillating nonlinearity, Rev. Mat. Univ. Complut. Madrid 23 (2010), no. 2, 321-339. pdf

Cazenave T., Dickstein F. and Weissler F.B., Structural properties of the set of global solutions of the nonlinear heat equation, in Current Advances in Nonlinear Analysis and Related Topics, 13--23, GAKUTO Internat. Ser. Math. Sci. Appl. 32, Gakkotosho, Tokyo, 2010. pdf

Cazenave T., Dickstein F. and Weissler F.B., Spectral properties of stationary solutions of the nonlinear heat equation, Publ. Mat. 55 (2011), no. 1, 185-200. pdf

Cazenave T., Fang D. and Han Z., Continuous dependence for NLS in fractional order spaces, Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 1, 135-147. pdf

Fang D., Xie J. and Cazenave T., Multiscale asymptotic behavior of the Schrödinger equation, Funk. Ekva. 54 (2011), no. 1, 69-94. pdf

Fang D., Xie J. and Cazenave T., Scattering for the focusing, energy-subcritical nonlinear Schrödinger equation, Sci. China Math. 54 (2011), no. 10, 2037-2062. pdf

Cazenave T., Dickstein F. and Weissler F.B., Multi-scale multi-profile global solutions of parabolic equations in RN, Discrete Contin. Dyn. Syst. Ser. S. 5 (2012), no. 3, 449-472. pdf

Cazenave T., Finite-time blowup for a family of nonlinear parabolic equations. Lecture notes prepared for VI ENAMA, Aracaju, Brazil, Nov. 7-9, 2012. pdf

Cazenave T., Escobedo M. and Zuazua E., Blowup for a time-oscillating nonlinear heat equation. Acta Math. Univ. Comenian. (N.S.) 82 (2013), no.1, 125-146. pdf

Cazenave T., Dickstein F. and Weissler F.B., Finite-time blowup for a complex Ginzburg-Landau equation, SIAM J. Math. Anal. 45 (2013), no. 1, 244-266. pdf

Cazenave T., Dickstein F. and Weissler F.B., Standing waves of the complex Ginzburg-Landau equation, Nonlinear Anal. 103 (2014), 26-32. pdf

Cazenave T., Dias J.P. and Figueira M., Finite-time blowup for a complex Ginzburg-Landau equation with linear driving. J. Evol. Equ. 14 (2014), no. 2, 403-415. pdf

Cazenave T., Correia S., Dickstein F. and Weissler F.B., A Fujita-type blowup result and low energy scattering for a nonlinear Schrödinger equation. São Paulo J. Math. Sci. 9 (2015), no. 2, 146-161. pdf

Cazenave T., Fang D. and Han Z., Local well-posedness for the H2-critical nonlinear Schrödinger equation. Trans. Amer. Math. Soc. 368 (2016), no. 11, 7911-7934. pdf

Cazenave T. and Naumkin I., Local existence, global existence, and scattering for the nonlinear Schrödinger equation. Commun. Contemp. Math. 19 (2017), no. 2, 1650038, 20 pp. pdf

Cazenave T., Dickstein F. and Weissler F.B., Non-regularity in Hölder and Sobolev spaces of solutions to the semilinear heat and Schrödinger equations. Nagoya Math. J. 226 (2017), 44-70. pdf

Cazenave T. and Naumkin I., Modified scattering for the critical nonlinear Schrödinger equation. J. Funct. Anal. 274 (2018), 402-432. pdf

Cazenave T. and Naumkin I., Spatial behavior for NLS and applications to scattering. Séminaire Laurent Schwartz-Équations aux dérivées partielles et applications. Année 2017-2018, Exp. No. I, 11 pp., Ed. Éc. Polytech., Palaiseau, 2018. pdf

Cazenave T., Martel Y. and Zhao L., Finite-time blowup for a Schrödinger equation with nonlinear source term. Discrete Cont. Dyn. Systems 39 (2019), no. 2, 1171-1183. pdf

Cazenave T., Dickstein F., Naumkin I. and Weissler F.B., Perturbations of self-similar solutions. Dyn. Partial Differ. Equ. 16 (2019), no. 2, 151-183. pdf

Cazenave T. and Snoussi S., Finite-time blowup for some nonlinear complex Ginzburg-Landau equations. In Partial Differential Equations Arising from Physics and Geometry, London Math. Soc. Lecture Note Ser., 450. Cambridge University Press, Cambridge, 2019, 172-214. pdf

Cazenave T., Martel Y. and Zhao L., Solutions with prescribed local blow-up surface for the nonlinear wave equation. Adv. Nonlinear Stud. 19 (2019), no. 4, 639-675. pdf

Cazenave T., Martel Y. and Zhao L., Solutions blowing up on any given compact set for the energy subcritical nonlinear wave equation. J. Differential Equations 268 (2020), no. 2, 680-706. pdf

Cazenave T. and Han Z., Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation. Discrete Cont. Dyn. Systems 40 (2020), no. 8, 4801--4819. pdf

Cazenave T., Dickstein F., Naumkin I. and Weissler F.B., Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value. Amer. J. Math. 142 (2020), no. 5, 1439-1495. pdf

Cazenave T., Dickstein F., Naumkin I. and Weissler F.B., Sign-changing solutions of the nonlinear heat equation with persistent singularities. ESAIM Control Optim. Calc. Var. 26 (2020), Art. 126, 35 pp. pdf

Cazenave T., Han Z. and Naumkin I., Asymptotic behavior for a dissipative nonlinear Schrödinger equation. Nonlinear Anal. 205 (2021), Art. No. 112243. pdf

Cazenave T. and Naumkin I., Local smooth solutions of the nonlinear Klein-gordon equation. Discrete Contin. Dyn. Syst. Ser. S. 14 (2021), no. 5, 1649-1672. pdf

Cazenave T., Han Z. and Martel Y., Blowup on an arbitrary compact set for a Schrödinger equation with nonlinear source term. J. Dynam. Differential Equations 33 (2021), no. 2, 941-960. pdf