Mes activités de recherche concernent les équations aux dérivées partielles non linéaires, elliptiques et paraboliques à données L1 ou mesure. Je m’intéresse en particulier aux questions d’existence, d’unicité et de stabilité des solutions de ces EDP à données peu régulières (le cadre L1 ou mesure n’étant pas le cadre classique variationnel). Les données L1 interviennent naturellement dans certains systèmes non linéaires couplés, statiques ou d’évolution, issus de la thermomécanique du solide, de la mécanique des fluides.

Publications

  • On Lewy Stampacchia inequalities for a pseudomonotone parabolic obstacle problem with L1-data, Olivier Guibé , Yassine Tahraoui et Guy Vallet, Nonlinear Analysis: Real World Applications, 77 (2024), pp.104030, [DOI]
  • Corrector results for a class of elliptic problems with nonlinear Robin conditions and data, Patrizia Donato, Olivier Guibé et Alip Oropeza, Networks and Heterogeneous Media 18 (2023): 1236-1259
  • Uniqueness for quasilinear elliptic problems in a two-component domain with L1 data, Rheadel Fulgencio et Olivier Guibé, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 211 (2021), 21 p.
  • Quasilinear Elliptic Problem in a Two-Component Domain with L1 data, Rheadel Fulgencio et Olivier Guibé, chapitre de Emerging Problems in the Homogenization of Partial Differential Equations (Donato P., Luna-Laynez M (eds)). SEMA SIMAI Springer Series, 10 (2021)
  • Nonlinear problems with unbounded coefficients and L1 data. Filomena Feo et Olivier Guibé, NoDEA, Nonlinear Differ. Equ. Appl. 27 49 (2020).
  • Lewy-Stampacchia’s inequality for a pseudo-monotone parabolic problem. Olivier Guibé, Abdelhafid Mokrane, Yassine Tahraoui et Guy Vallet. Advances in Nonlinear Analysis 9 (2020), 591-612.
  • Uniqueness for Neumann problems for nonlinear elliptic equations. Maria Francesca Betta, Olivier Guibé et Anna Mercaldo. Commun. Pure Appl. Anal. 18 (2019), No. 3, 1023-1048.
  • Homogenization of quasilinear elliptic problems with nonlinear Robin conditions and L1 data. Patrizia Donato, Olivier Guibé et Alip Oropeza. Journal de Mathématiques Pures et Appliqués 120 (2018) , 91-129.
  • Symmetry and asymmetry of minimizers of a class of noncoercive functionals. Friedemann Brock, Gisella Croce, Olivier Guibé et Anna Mercaldo. Advances in Calculus of Variations (à paraître) [DOI] [PDF]
  • Homogenization of an evolution problem with L log L data in a domain with oscillating boundary. Antonio Gaudiello et Olivier Guibé. Annali di Matematica Pura ed Applicata (4) 197 (2018), No. 1, 153-169.
  • Homogenization of the brush problem with a source term in L1. Antonio Gaudiello, Olivier Guibé et François Murat. Archive for Rational Mechanics and Analysis 225 (2017), Issue 1, 1-64.
  • Renormalized solutions of elliptic equations with Robin boundary conditions. Olivier Guibé et Alip Oropeza. Acta Mathematica Scientia 37 (2017), Issue 4, 889–910.
  • Uniqueness for elliptic problems with locally lipschitz continuous dependence on the solution. Filomena Feo et Olivier Guibé. J. Differential Equations 262 (2017), Issue 3, 1777-1798.
  • Existence and uniqueness of a solution for a class of parabolic equations with two unbounded nonlinearities. Dominique Blanchard, Olivier Guibé et Hicham Redwane. Commun. Pure Appl. Anal. 15 (2016), Issue 1, 197–217.
  • Renormalized solution of elliptic equations with Neumann boundary conditions. Maria Francesca Betta, Anna Mercaldo et Olivier Guibé. J. Differential Equations 259 (2015), Issue 3, 898–924 [PDF]
  • Homogenization of an elliptic second-order problem with \(L \log L\) data in a domain with oscillating boundary. Antonio Gaudiello et Olivier Guibé. Communications in Contemporary Mathematics 15, 1350008 (2013), 13 pages.
  • Uniqueness of renormalized solutions to nonlinear parabolic problems with lower order terms. Rosaria Di Nardo, Filomena Feo et Olivier Guibé. Proceedings of the Royal Society of Edinburgh, Section: A Mathematics 143 (2013), no. 143, 1185–1208. [PDF]
  • Uniqueness result for nonlinear anisotropic elliptic equations. Rosaria Di Nardo, Filomena Feo et Olivier Guibé. Advances in Differential Equations 18 (2013), no. 5-6, 433–458.
  • Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation. Dominique Blanchard, Nicolas Bruyère et Olivier Guibé. Commun. Pure Appl. Anal. 12 (2013), no. 5, 2213–2227.
  • Existence result for nonlinear parabolic equations with lower order terms. Di Nardo, Rosaria ; Feo, Filomena ; Guibé, Olivier. Anal. Appl. (Singap.) 2 (2011), no 2, pp 161-186. [PDF]
  • Weak-renormalized solution for a nonlinear Boussinesq system. Abdelatif, Attaoui ; Blanchard, Dominique ; Guibé, Olivier. Differential Integral Equations 22 (2009), no. 5-6, pp 465–494. [PDF]
  • Uniqueness of the renormalized solution to a class of nonlinear elliptic equations. Guibé Olivier. Quaderni di Matematica, 23. Department of Mathematics, Seconda Università di Napoli, Caserta (2008) [PDF]
  • Nonlinear equations with unbounded heat conduction and integrable data. Blanchard, Dominique ; Guibé, Olivier ; Redwane, Hicham. Ann. Mat. Pura Appl (4) 187 (2008), no. 3 pp 405–433. [PDF]
  • Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms. Guibé, Olivier ; Mercaldo, Anna. Commun. Pure Appl. Anal. 7 (2008), no. 1, pp 163–192. [PDF]
  • Existence of renormalized solutions to nonlinear elliptic equations with two lower order terms and measure data. Guibé, Olivier ; Mercaldo, Anna. Trans. Amer. Math. Soc. 360, no. 2, 2008 pp 643–669. [PDF]
  • Uniqueness of the solution to quasilinear elliptic equations under a local condition on the diffusion matrix. Guibé Olivier. Adv. Math. Sci. Appl. 17 (2007), no. 2, pp 357–368. [PDF]
  • Existence and stability results for renormalized solutions to noncoercive nonlinear elliptic equations with measure data. Guibé, Olivier ; Mercaldo, Anna. Potential Anal. 25 (2006), no. 3, pp. 223–258. [PDF]
  • Nonlinear and non-coercive elliptic problems with integrable data. Ben Cheikh Ali, Mohsen ; Guibé, Olivier. Adv. Math. Sci. Appl. 16 (2006), no. 1, pp. 275–297. [PDF]
  • Quasi-linear degenerate elliptic problems with L1 data. Blanchard, Dominique ; Désir, François ; Guibé, Olivier. Nonlinear Anal. 60 (2005), no. 3, pp. 557–587. [PDF]
  • Infinite valued solutions of non-uniformly elliptic problems. Blanchard, Dominique ; Guibé, Olivier. Anal. Appl. (Singap.) 2 (2004), no. 3, pp. 227–246. [PDF]
  • Existence and uniqueness results for a nonlinear stationary system. Guibé Olivier. NoDEA Nonlinear Differential Equations Appl. 10 (2003), no. 3, pp. 309–328. [PDF]
  • Remarks on the uniqueness of comparable renormalized solutions of elliptic equations with measure data. Guibé Olivier. Ann. Mat. Pura Appl (4) 180 (2002), no. 4, pp. 441–449. [PDF]
  • Existence of a solution for a nonlinear system in thermoviscoelasticity. Blanchard, Dominique ; Guibé, Olivier. Adv. Differential Equations 5 (2000), no. 10-12, pp. 1221–1252.
  • Résultats d’existence et d’unicité pour une classe de problèmes non linéaires et non coercifs. Ben Cheikh Ali, Mohsen ; Guibé, Olivier. C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 11, pp. 967–972.
  • Solutions entropiques et renormalisées pour un système non linéaire couplé. Guibé Olivier. C.R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 6, pp. 685–690.
  • Existence d’une solution pour un système non linéaire en thermoviscoélasticité. Blanchard, Dominique ; Guibé, Olivier. C.R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 10, pp. 1125–1130.

Thèse et HDR

  • Solutions renormalisées pour des équations elliptiques, paraboliques et des systèmes couplés. Habilitation à Diriger des Recherches, soutenue le 10 décembre 2010 à l’Université de Rouen. [PDF]
  • Existence de solutions pour des systèmes couplés non linéaires elliptiques ou d’évolution. Thèse de Doctorat soutenue à l’Université de Rouen, janvier 1998. [PDF]