Research Interests

  • Partial Differential Equations: Nonlinear diffusion equations, non-homogeneous media, semilinear elliptic problems, semigroups of operators and spectral theory.
  • Mathematical Physics: Mechanics and Electromagnetic Theory. Lagrangian variational approach in Electromagnetics Theory.
  • Consulting in Data Analysis and Machine Learning.

 

List of Publications

  • J.A. Goldstein & G. Reyes, Equipartition of energy for an ill-posed system with cross fricton, in preparation.
  • A. Castro & G. Reyes, Existence of multiple solutions for a semilinear problem and a counterexample by E. N. Dancer, submitted to Commun. Pure Appl. Analysis
  • A. Figotin & G. Reyes, Lagrangian Variational Framework for Boundary Value Problems, J. Math. Phys. 56, 093506 (2015)
  • J.A. Goldstein, Gisele Ruiz Goldstein & G. Reyes, Overdamping and energy decay for abstract wave equations with strong damping, Asymptot. Anal. 88 (4) (2014), pp 217-232.
  • A. Figotin & G. Reyes, Multi-transmission-line-beam interactive system. Journal of Mathematical Physics 54, 111901 (2013).
  • R. G. Iagar, G. Reyes & A. Sanchez, Radial Equivalence of Nonhomogeneous Nonlinear Diffusion Equations, Acta Applicandae Mathematicae 123 (1) (2013), pp. 53-72.
  • J.A. Goldstein & G. Reyes, Equipartition of operator-weighted energies in damped wave equations, Asymptotic Analysis 81 (2) (2013), pp. 171-187.
  • A. de Pablo, G. Reyes & A. Sanchez, Blow-up for a nonhomogeneous heat equation with reaction, DCDS-A 33 (2) (2013), pp. 643-662.
  • S. Elena Nieto & G. Reyes, Asymptotic behavior of the solutions of the inhomogeneous Porous Medium Equation with critical vanishing density, Commun. Pure Appl. Anal. 12 (2) (2013), pp. 1123-1139.
  • S. Kamin, G. Reyes & J. L. Vazquez, Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density, Discrete and Continuous Dynamical Systems, (special issue devoted to Nonlinear Parabolic Problems), DCDS-A 26 (2) (2010), pp. 521-549.
  • A. Bouzelmate, A. Gmira & G. Reyes, On the radial solutions of a degenerate elliptic equation with convection term, Int. J. Math. Anal. (Ruse) 1 (2007), no. 17-20, pp. 975-993.
  • A. Bouzelmate, A. Gmira & G. Reyes, On the self-similar solutions for a nonlinear Ornstein- Uhlenbeck equation, Electronic Journal of Differential Equations 67 (2007), pp. 1-21.
  • A. de Pablo, G. Reyes & A. Sanchez, Blow-up for a heat equation with convection and boundary flux, Proc. Roy. Soc. Edinburgh Sect. A 138 (3) (2008), pp. 513-530.
  • G. Reyes & J. L. Vazquez, The inhomogeneous PME in several space dimensions. Existence and uniqueness of nite energy solutions, Commun. Pure Appl. Anal. 7 (6) (2008), pp. 1275-1294.
  • G. Reyes & J. L. Vazquez, Long time behaviour for the inhomogeneous PME in a medium with slowly decaying density, Commun. Pure Appl. Anal. 8 (2) (2009), pp 493-508.
  • G. Reyes & J. L. Vazquez, The Cauchy problem for the inhomogeneous porous medium equation, Networks and Heterogeneous Media 1 (2) (2006), pp. 337-351.
  • G. Reyes & J. L. Vazquez, A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media, J. Eur. Math. Soc. 8 (2006), pp. 531-554.
  • G. Reyes & A. Tesei, Self-Similar Solutions of a Semilinear Parabolic Equation with Inverse-Square Potential, J. Differential Equations 219 (2005), pp. 40-77.
  • L. Moschini, G. Reyes & A. Tesei, Nonuniqueness of solutions to a semilinear parabolic equation with inverse-square potential, Commun. Pure Appl. Anal. 5 (1) (2006), pp. 155-179.
  • R. Ferreira, A. de Pablo, G. Reyes & A. Sanchez, The interfaces of an inhomogeneous porous medium equation with convection, Comm. Partial Differential Equations 31 (2006), pp. 1-18.
  • A. de Pablo & G. Reyes, Long time behaviour for a nonlinear rst order equation, Nonlinear Anal.TMA 65 (2) (2006), pp. 284-300.
  • G. Reyes & A. Sanchez, Disappearance of interfaces for the porous medium equation with variable density and absorption, Asymptotic Analysis 36 (2003), pp. 13-20.
  • G. Reyes & A. Tesei, Basic theory for a diffusion-absorption equation in an inhomogeneous medium, Nonlinear Differential Equations Appl. 10 (2) (2003), pp. 197-222.
  • R. Kersner, G. Reyes & A. Tesei, On a class of parabolic equations with variable density and absorption, Adv. Differential Equations 7 (2) (2002), pp. 155-176.
  • G. Reyes, Critical asymptotic behaviour for a perturbed conservation law, Asymptotic Analysis 25 (2001), pp. 109-122.
  • G. Reyes & J. L. Vazquez, Asymptotic behaviour for a generalized Burgers’ Equation, J. Math. Pures Appl. 78 (1999), pp. 633-666.
  • G. Reyes, Asymptotic behaviour of diffusion-convection processes, Nonlinear Anal. 37 (1999), pp.301-318.