Books (1)

  1. Nonlinear Reaction-Diffusion Processes for Nanocomposites
    J.I. DíazD. Gómez-Castro, and T. A Shaposhnikova
    De Gruyter

Preprints (6)

  1. P6
    Beginner’s guide to Aggregation-Diffusion Equations
    David Gómez-Castro
  2. P5
    A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains
    Rafael BailoJosé A. Carrillo, Stefano Fronzoni, and David Gómez-Castro
  3. P4
    Partial mass concentration for fast-diffusions with non-local aggregation terms
    José A. CarrilloA. Fernández-Jiménez, and D. Gómez-Castro
  4. P3
    Singular solutions for space-time fractional equations in a bounded domain
    Hardy ChanDavid Gómez-Castro, and Juan Luis Vázquez
  5. P2
    Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence
    Lucio Boccardo, David Gómez-Castro, and Jesús Ildefonso Díaz
  6. P1
    Interpreting systems of continuity equations in spaces of probability measures through PDE duality
    José A. Carrillo, and David Gómez-Castro

Journal Articles (34)

  1. J34
    Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel
    José A. CarrilloD. Gómez-CastroYao Yao, and Chongchun Zeng
    Archive for Rational Mechanics and Analysis, 2023
  2. J33
    Singular boundary behaviour and large solutions for fractional elliptic equations
    Nicola AbatangeloD. Gómez-Castro, and J.L. Vázquez
    Journal of the London Mathematical Society, 2023
  3. J32
    Singular solutions for fractional parabolic boundary value problems
    Hardy ChanDavid Gómez-Castro, and Juan Luis Vázquez
    Revista de la Real Academia de Ciencias Exactas, Fı́sicas y Naturales. Serie A. Matemáticas, 2022
  4. J31
    A fast regularisation of a Newtonian vortex equation
    José A. CarrilloD. Gómez-Castro, and J.L. Vázquez
    Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 2022
  5. J30
    Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
    Jose A. CarrilloDavid Gómez-Castro, and Juan Luis Vázquez
    Advances in Nonlinear Analysis, 2022
  6. J29
    Infinite-time concentration in aggregation–diffusion equations with a given potential
    J.A. CarrilloD. Gómez-Castro, and J.L. Vázquez
    Journal de Mathématiques Pures et Appliquées, 2022
  7. J28
    Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
    Félix del TesoD. Gómez-Castro, and J.L. Vázquez
    Fract. Calc. Appl. Anal., 2021
  8. J27
    Characterisation of homogeneous fractional Sobolev spaces
    Lorenzo Brasco, D. Gómez-Castro, and J.L. Vázquez
    Calculus of Variations and Partial Differential Equations, 2021
  9. J26
    Steiner symmetrization for anisotropic quasilinear equations via partial discretization
    Friedemann BrockJ.I. Díaz, Adele Ferone, D. Gómez-Castro, and Anna Mercaldo
    Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 2021
  10. J25
    Blow-up phenomena in nonlocal eigenvalue problems: When theories of L^1 and L^2 meet
    Hardy ChanD. Gómez-Castro, and J.L. Vázquez
    Journal of Functional Analysis, 2021
  11. J24
    Estimates on translations and Taylor expansions in fractional Sobolev spaces
    Félix del TesoD. Gómez-Castro, and J.L. Vázquez
    Nonlinear Anal., 2020
  12. J23
    A Time-Dependent Strange Term Arising in Homogenization of an Elliptic Problem with Rapidly Alternating Neumann and Dynamic Boundary Conditions Specified at the Domain Boundary: The Critical Case
    J. I. DíazD. Gómez-Castro, T. A. Shaposhnikova, and M. N. Zubova
    Dokl. Math., 2020
  13. J22
    Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes
    J.I. DíazD. Gómez-Castro, Alexander V Podolskiy, and T. A Shaposhnikova
    Adv. Nonlinear Anal., 2020
  14. J21
    The fractional Schrödinger equation with singular potential and measure data
    D. Gómez-Castro, and J.L. Vázquez
    Discret. Contin. Dyn. Syst. - A, 2019
  15. J20
    A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition
    J.I. DíazD. Gómez-Castro, T. A. Shaposhnikova, and Maria N. Zubova
    Electron. J. Differ. Equ., 2019
  16. J19
    On the well-posedness of a multiscale mathematical model for Lithium-ion batteries
    J. I. DíazD. Gómez-Castro, and Angel M. Ramos
    Adv. Nonlinear Anal., 2018
  17. J18
    Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition
    J. I. DíazD. Gómez-Castro, Alexander V Podol’skii, and T. A Shaposhnikova
    Adv. Nonlinear Anal., 2019
  18. J17
    Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles
    J. I. DíazD. Gómez-Castro, T. A. Shaposhnikova, and M. N. Zubova
    Appl. Anal., 2019
  19. J16
    The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach
    J. I. DíazD. Gómez-Castro, and J. L. Vázquez
    Nonlinear Anal., 2018
  20. J15
    Homogenization of Boundary Value Problems in Plane Domains with Frequently Alternating Type of Nonlinear Boundary Conditions: Critical Case
    J. I. DíazD. Gómez-Castro, A. V. Podolskiy, and T. A. Shaposhnikova
    Dokl. Math., 2018
  21. J14
    Study of tumor growth indicates the existence of an “immunological threshold” separating states of pro- and antitumoral peritumoral inflammation
    Antonio Brú, D. Gómez-Castro, Luis Vila, Isabel Brú, and Juan Carlos Souto
    PLoS One, 2018
  22. J13
    Non existence of critical scales in the homogenization of the problem with p-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in n-dimensional domains when p>n
    J. I. DíazD. Gómez-Castro, A. V. Podolskii, and T. A. Shaposhnikova
    Rev. la Real Acad. Ciencias Exactas, Físicas y Nat. Ser. A. Matemáticas, 2018
  23. J12
    Existence and uniqueness of solutions of Schrödinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications
    J.I. DíazD. Gómez-Castro, and J.-M. Rakotoson
    Differ. Equations Appl., 2018
  24. J11
    Linear diffusion with singular absorption potential and/or unbounded convective flow: The weighted space approach
    R. Temam, J. M. Rakotoson, D. Gómez-Castro, and J. I. Díaz
    Discrete and Continuous Dynamical Systems, 2018
  25. J10
    Change of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size
    J.I. DíazD. Gómez-Castro, T. A. Shaposhnikova, and M. N. Zubova
    Electronic Journal of Differential Equations, 2017
  26. J09
    On the asymptotic limit of the effectiveness of reaction–diffusion equations in periodically structured media
    J.I. DíazD. Gómez-Castro, A.V. Podolskii, and T.A. Shaposhnikova
    Journal of Mathematical Analysis and Applications, 2017
  27. J08
    Homogenization of variational inequalities of Signorini type for the p-Laplacian in perforated domains when p ∈(1, 2)
    J.I. DíazD. Gómez-Castro, A. V. Podol’skii, and T. A. Shaposhnikova
    Doklady Mathematics, 2017
  28. J07
    Visibility to discern local from nonlocal dynamic processes
    Antonio Brú, D. Gómez-Castro, and J.C. Nuño
    Physica A: Statistical Mechanics and its Applications, 2017
  29. J06
    Shape differentiation of a steady-state reaction-diffusion problem arising in Chemical Engineering: the case of non-smooth kinetic with dead core
    D. Gómez-Castro
    Electronic Journal of Differential Equations, 2017
  30. J05
    Rigidity of optimal bases for signal spaces
    Haïm Brezis, and D. Gómez-Castro
    Comptes Rendus Mathematique, 2017
  31. J04
    Homogenization of the p-Laplace operator with nonlinear boundary condition on critical size particles: identifying the strange terms for some non smooth and multivalued operators
    J.I. DíazD. Gómez-Castro, A. V. Podol’skii, and T. A. Shaposhnikova
    Doklady Mathematics, 2016
  32. J03
    On the Effectiveness of Wastewater Cylindrical Reactors: an Analysis Through Steiner Symmetrization
    J.I. Díaz, and D. Gómez-Castro
    Pure and Applied Geophysics, 2016
  33. J02
    The Effectiveness Factor of Reaction-Diffusion Equations: Homogenization and Existence of Optimal Pellet Shapes
    J.I. DíazD. Gómez-Castro, and Claudia Timofte
    Journal of Elliptic and Parabolic Equations, 2016
  34. J01
    An Application of Shape Differentiation to the Effectiveness of a Steady State Reaction-Diffusion Problem Arising in Chemical Engineering
    J.I. Díaz, and D. Gómez-Castro
    Electronic Journal of Differential Equations, 2015

Conference Proceedings

  1. C03
    On the influence of pellet shape on the effectiveness factor of homogenized chemical reactions
    J.I. DíazD. Gómez-Castro, and Claudia Timofte
    In Proceedings Of The XXIV Congress On Differential Equations And Applications XIV Congress On Applied Mathematics, 2015
  2. C02
    Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem
    D. Gómez-Castro, and J.I. Díaz
    In Dynamical Systems and Differential Equations, Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015
  3. C01
    A mathematical proof in nanocatalysis: better homogenized results in the diffusion of a chemical reactant through critically small reactive particles
    J.I. Díaz, and D. Gómez-Castro
    In Progress in Industrial Mathematics at ECMI 2016, 2017


  1. Foreword to Special Issue in Honour Juan Luis Vázquez. Discrete and Continuous Dynamical Systems 43 (3&4)
    José A. CarrilloFélix del Teso, and David Gómez-Castro
  1. Homogenization and Shape Differentiation of Quasilinear Elliptic Equations
    D. Gómez-Castro
    Facultad de Matemáticas, Universidad Complutense de Madrid, 2017
    PhD Dissertation