Publications

Preprints

  • Gómez-Castro, D., & Vázquez, J. L.
    The fractional Schrödinger equation with singular potential and measure data.
    arXiv:1812.02120

Online first

Journal articles

2020

  • 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

  • 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.
    Journal: website
    arXiv:1905.11709
  • 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
  • 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
  • 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

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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

  • 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.
  • 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
  • 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
  • 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
  • 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.
    http://arxiv.org/abs/1708.01041
  • 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

  • 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
  • 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
  • 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

  • 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

  • Díaz, J. I., & Gómez-Castro, D. (2017).
    A Mathematical Proof in Nanocatalysis: Better Homogenized Results in the Diffusion of a Chemical Reactant Through Critically Small Reactive Particles.
    In P. Quintela, P. Barral, D. Gómez, F. J. Pena, J. Rodríguez, P. Salgado, & M. E. Vázquez-Mendez (Eds.),
    Progress in Industrial Mathematics at ECMI 2016(pp. 319–326). Springer.
    doi:10.1007/978-3-319-63082-3_49
  • Gómez-Castro, D., & Díaz, J. I. (2015).
    Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem. In Dynamical Systems and Differential Equations,
    AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain)
    (pp. 379–386). American Institute of Mathematical Sciences.
    doi:10.3934/proc.2015.0379
  • Díaz, J. I., Gómez-Castro, D., & Timofte, C. (2015).
    On the influence of pellet shape on the effectiveness factor of homogenized chemical reactions.
    In Proceedings Of The XXIV Congress On Differential Equations And Applications XIV Congress On Applied Mathematics(pp. 571–576).

Other

  • Gómez-Castro, D. (2017).
    Homogenization and Shape Differentiation of Quasilinear Elliptic Equations.
    Thesis at Universidad Complutense de Madrid.
    arXiv:1712.10074