Publications

Books

  1. Jesús Ildefonso Díaz, David Gómez-Castro and Tatiana A. Shaposhnikova
    Nonlinear Reaction-Diffusion Processes for Nanocomposites
    De Gruyter. In press (see Amazon)

Preprints

  • Carrillo, J. A., Gómez-Castro, D., Yao, Y., & Zeng C. (2021)
    Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel
    arxiv: 2105.13323
  • Carrillo, J. A., Gómez-Castro, D., & Vázquez, J.L. (2021).
    Infinite-time concentration in Aggregation–Diffusion equations with a given potential
    arxiv: 2103.12631
  • del Teso, F., Gómez-Castro, D., & Vázquez, J. L. (2020).
    Three representations of the fractional $p$-Laplacian: semigroup, extension and rBalakrishnan formulas.
    arxiv:2010.06933
  • Chan, H., Gómez-Castro, D., & Vázquez, J. L. (2020).
    Singular solutions for fractional parabolic boundary value problems
    arxiv:2007.13391
  • Carrillo J.A., Gómez-Castro D, & Vázquez, J. L. (2020).
    Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
    arxiv:2007.01185.
  • Carrillo, J. A., Gómez-Castro, D. & Vázquez, J. L . (2019).
    A fast regularisation of a Newtonian vortex equation
    arxiv:1912.00912
  • Abatangelo, N., Gómez-Castro, D., & Vázquez, J. L. (2019).
    Singular boundary behaviour and large solutions for fractional elliptic equations.
    arxiv:1910.00366

Journal articles

Online first

Published

2021

  1. Brasco, L., Gómez-Castro, D., & Vázquez, J. L. (2021).
    Characterisation of homogeneous fractional Sobolev spaces.
    Calculus of Variations and Partial Differential Equations
    doi: 10.1007/s00526-021-01934-6
    arxiv:2007.08000
  2. Brock, F., Díaz, J. I., Ferone, A., Gómez-Castro, D., & Mercaldo, A. (2021).
    Steiner symmetrization for anisotropic quasilinear equations via partial discretization.
    Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 38(2), 347–368.
    doi:10.1016/j.anihpc.2020.07.005
    arxiv:1912.02080
  3. Chan, H., Gómez-Castro, D., & Vázquez, J. L. (2021).
    Blow-up phenomena in nonlocal eigenvalue problems: when theories of $L^1$ and $L^2$ meet
    Journal of Functional Analysis, 280(7), 108845
    doi:10.1016/j.jfa.2020.108845
    arxiv:2004.04579

2020

  1. del Teso, F. , Gómez-Castro, D., & Vázquez, J. L. (2020)
    Estimates on translations and Taylor expansions in fractional Sobolev spaces.
    Nonlinear Analysis, 200, 111995
    doi:10.1016/j.na.2020.111995
    arxiv:2004.12196
  2. Díaz, J. I., Gómez-Castro, D. , Shaposhnikova, T. A., & Zubova, M. N. (2020)
    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
    Doklady Mathematics, 101(2), 96–101.
    doi:10.1134/S106456242002009X
  3. Díaz, J. I., Gómez-Castro, D., Podolskiy, A. V, & Shaposhnikova, T. A. (2020).
    Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes.
    Advances in Nonlinear Analysis, 9(1), 193–227.
    doi:10.1515/anona-2018-0158

2019

  1. Gómez-Castro, D., & Vázquez, J. L. (2019).
    The fractional Schrödinger equation with singular potential and measure data.
    Discrete & Continuous Dynamical Systems – A, 39(12), 7113–7139.
    doi:10.3934/dcds.2019298
    arXiv:1812.02120
  2. Díaz, J. I., Gómez-Castro, D., Shaposhnikova, T. A., & Zubova, M. N. (2019)
    A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition.
    Electron. J. Differential Equations. 2019(77), 1-13.
    arXiv:1905.11709
  3. Díaz, J. I., Gómez-Castro, D., & Ramos, A. M. (2019)
    On the well-posedness of a multiscale mathematical model for Lithium-ion batteries.
    Advances in Nonlinear Analysis. 8(1), 1132–1157
    doi:10.1515/anona-2018-0041
  4. Díaz, J. I., Gómez-Castro, D., Podol’skii, A. V, & Shaposhnikova, T. A. (2019).
    Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition.
    Advances in Nonlinear Analysis, 8(1), 679–693.
    doi:10.1515/anona-2017-0140
  5. Díaz, J. I., Gómez-Castro, D., Shaposhnikova, T. A., & Zubova, M. N. (2019).
    Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles.
    Applicable Analysis, 98(1–2), 232–255.
    doi:10.1080/00036811.2018.1441997

2018

  1. Díaz, J. I., Gómez-Castro, D., & Vázquez, J. L. (2018).
    The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach.
    Nonlinear Analysis, 177, 325–360.
    doi:10.1016/j.na.2018.05.001
  2. Díaz, J. I., Gómez-Castro, D., Podolskiy, A. V., & Shaposhnikova, T. A. (2018).
    Homogenization of Boundary Value Problems in Plane Domains with Frequently Alternating Type of Nonlinear Boundary Conditions: Critical Case.
    Doklady Mathematics, 97(3). 271-276
    doi:10.1134/S1064562418030225
  3. Brú, A., Gómez-Castro, D., Vila, L., Brú, I., & Souto, J. C. (2018).
    Study of tumor growth indicates the existence of an “immunological threshold” separating states of pro- and antitumoral peritumoral inflammation.
    PLOS ONE, 13(11), e0202823.
    doi:10.1371/journal.pone.0202823
  4. Díaz, J. I., Gómez-Castro, D., Podolskii, A. V., & Shaposhnikova, T. A. (2018).
    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.
    Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales – Serie A: Matematicas, 112(2) 331-340.
    doi:10.1007/s13398-017-0381-z
  5. Díaz, J. I., Gómez-Castro, D., & Rakotoson, J.-M. (2018).
    Existence and uniqueness of solutions of Schrödinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications.
    Differential Equations & Applications, 10(1), 47–74.
    doi:10.7153/dea-2018-10-04
  6. Díaz, J.I., Gómez-Castro, D., Temam, R., & Rakotoson, J. M., (2018).
    Linear diffusion with singular absorption potential and/or unbounded convective flow: The weighted space approach.
    Discrete and Continuous Dynamical Systems, 38(2), 509–546.
    doi:10.3934/dcds.2018023

2017

  1. Díaz, J. I., Gómez-Castro, D., Shaposhnikova, T. A., & Zubova, M. N. (2017).
    Change of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size.
    Electronic Journal of Differential Equations, 2017.
  2. Díaz, J. I., Gómez-Castro, D., Podolskii, A. V., & Shaposhnikova, T. A. (2017).
    On the asymptotic limit of the effectiveness of reaction–diffusion equations in periodically structured media.
    Journal of Mathematical Analysis and Applications, 455(2).
    doi:10.1016/j.jmaa.2017.06.036
  3. Díaz, J. I., Gómez-Castro, D., Podolskiy, A. V., & Shaposhnikova, T. A. (2017).
    Homogenization of variational inequalities of Signorini type for the p-Laplacian in perforated domains when p ∈ (1, 2).
    Doklady Mathematics, 95(2).
    doi:10.1134/S1064562417020132
  4. Brú, A., Gómez-Castro, D., & Nuño, J. C. (2017).
    Visibility to discern local from nonlocal dynamic processes.
    Physica A: Statistical Mechanics and its Applications, 471.
    doi:10.1016/j.physa.2016.12.078
  5. Gómez-Castro, D. (2017).
    Shape differentiation of a steady-state reaction-diffusion problem arising in Chemical Engineering: the case of non-smooth kinetic with dead core.
    Electronic Journal of Differential Equations, 2017(221), 1–11.
    arXiv:1708.01041
  6. Brezis, H., & Gómez-Castro, D. (2017).
    Rigidity of optimal bases for signal spaces.
    Comptes Rendus Mathematique, 355(7).
    doi:10.1016/j.crma.2017.06.004

2016

  1. Díaz, J. I., Gómez-Castro, D., Podol’skii, A. V, & Shaposhnikova, T. A. (2016).
    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.
    Doklady Mathematics, 94(1), 387–392.
    doi:10.1134/S1064562416040098
  2. Díaz, J. I., & Gómez-Castro, D. (2016).
    On the Effectiveness of Wastewater Cylindrical Reactors: an Analysis Through Steiner Symmetrization.
    Pure and Applied Geophysics, 173(3).
    doi:10.1007/s00024-015-1124-8
  3. Díaz, J. I., Gómez-Castro, D., & Timofte, C. (2016).
    The Effectiveness Factor of Reaction-Diffusion Equations: Homogenization and Existence of Optimal Pellet Shapes.
    Journal of Elliptic and Parabolic Equations, 2(1–2), 119–129.
    doi:10.1007/BF03377396

2015

  1. Díaz, J. I., & Gómez-Castro, D. (2015).
    An Application of Shape Differentiation to the Effectiveness of a Steady State Reaction-Diffusion Problem Arising in Chemical Engineering.
    Electronic Journal of Differential Equations, 22, 31–45.

Conferences papers

Other