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.
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.
- J. I. Díaz, D. 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. https://doi.org/10.1515/anona-2017-0140
- 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: https://doi.org/10.1515/anona-2018-0041.
- J. I. Díaz, D. 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. https://doi.org/10.1080/00036811.2018.1441997
- 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: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
- J. I. Díaz, D. 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: https://doi.org/10.1515/anona-2018-0158