Institutos Universitarios

David Gómez Castro

Profesor ayudante doctor (Assistant Professor)
Department of Applied Mathematics and Mathematical Analysis
School of Mathematical Sciences
Complutense University of Madrid
Research Group MOMAT
Nonlinear PDEs and applications




I am currently an Assistant Professor at the Department of Applied Mathematics and Mathematical Analysis at Universidad Complutense de Madrid. I completed my Ph.D. in Mathematical Engineering, Statistics and Operational Research under Prof. J.I. Díaz at Universidad Complutense de Madrid in 2017, supported by an FPU Grant. I received my M.Sc. and Bachelor Degrees in Mathematics from Universidad Complutense de Madrid. During 2018 I was Assistant Professor at the ICAI School of Engineering of Universidad Pontificia de Comillas. In 2018 I was awarded the Vicent Caselles Prize by RSME and Fundación BBVA.


Research interests

Local and non-local semilinear parabolic and elliptic problems (in particular Brézis’ theory of very weak solutions), homogenisation problems, rearrangement theory (Schwarz and Steiner), shape optimisation and differentiation.


Last Publications

  • J. I. DíazD. Gómez-Castro, A. V. Podol’skii, T. A. Shaposhnikova. Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition. Advances in Nonlinear Analysis. 2019, 8, 679-693.
  • J. I. Díaz, D. Gómez-Castro, A. M. Ramos, On the well-posedness of a multiscale mathematical model for Lithium-ion batteries. Advances in Nonlinear Analysys, ISSN: 2191-9496, 2019; 8: 1132--1157. DOI link:
  • J. I. DíazD. Gómez-Castro, T. A. Shaposhnikova, M. N. Zubova. Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles. Applicable Analysis, 98(1–2) (2019), 232–255.
  • J. I. Díaz, D. Gómez-Castro, T. A. Shaposhnikova, M. N. Zubova. A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions. Electronic Journal of Di erential Equations. Vol. 2019 (2019), No. 77, pp. 1--13. ISSN: 1072-6691. URL: or
  • J. I. DíazD. Gómez-Castro, A. V. Podolskiy, T. A. Shaposhnikova. Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes. Advances in Nonlinear Analysis. 9(2020), no. 1, 193--227 doi: