Dr David Gomez Castro

PhD, MSc, BSc

Contact form

https://gomezcastro.xyz

+44 1865 615105

ORCID iD

https://orcid.org/0000-0001-8360-3250

Research groups

Oxford Centre for Nonlinear PDE

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Recent books

Nonlinear Reaction-Diffusion Processes for Nanocomposites Anomalous Improved Homogenization Díaz, J Gómez-Castro, D Shaposhnikova, T (21 Jun 2021)

Teaching

I am currently an Stipendiary Lecturer at Queen's

Research interests

I research the properties of Partial Differential Equations of aggregation-diffusion-reaction type. I am interested in the analytical properties of the solutions (existence, uniqueness, integrability, a priori estimates...), as well as their their numerical analysis. I am also interest in fractional Laplacians, homogenisation and the properties of Sobolev spaces.

Recent publications

Asymptotic simplification of Aggregation-Diffusion equations towards the
heat kernel

Carrillo, J Gómez-Castro, D Yao, Y Zeng, C Archive for Rational Mechanics and Analysis (01 Nov 2022) http://arxiv.org/abs/2105.13323v1

Singular solutions for fractional parabolic boundary value problems

Chan, H Gomez Castro, D Vázquez, J Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas volume 116 issue 4 (01 Aug 2022)

Interpreting systems of continuity equations in spaces of probability
measures through PDE duality

Carrillo, J Gómez-Castro, D (08 Jun 2022) http://arxiv.org/abs/2206.03968v1

A fast regularisation of a Newtonian vortex equation

Carrillo, J Gómez-Castro, D Vázquez, J Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire (02 Dec 2019) http://arxiv.org/abs/1912.00912v2

Vortex formation for a non-local interaction model with Newtonian
repulsion and superlinear mobility

Carrillo, J Gómez-Castro, D Vázquez, J Advances in Nonlinear Analysis http://arxiv.org/abs/2007.01185v2

Prizes, awards, and scholarships

Vicent Caselles Prize 2018, Real Sociedad Matemática Española and Fundación BBVA