11 citations · 18 across the 8 of their papers we have counts for
8 papers
Drift-diffusion equations with saturation
José Antonio Carrillo, Alejandro Fernández-Jiménez, David Gómez-Castro
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density with a continuous and compactly supported nonlinear mobility …
Aggregation-Diffusion Equations for Collective Behaviour in the Sciences
Rafael Bailo, José A. Carrillo, David Gómez-Castro
This is a survey article based on the content of the plenary lecture given by José A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state…
Beginner's guide to Aggregation-Diffusion Equations
David Gómez-Castro
The aim of this survey is to serve as an introduction to the different techniques available in the broad field of Aggregation-Diffusion Equations. We aim to provide historical cont…
A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains
Rafael Bailo, José A. Carrillo, Stefano Fronzoni +1
We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct pr…
Partial mass concentration for fast-diffusions with non-local aggregation terms
José A. Carrillo, A. Fernández-Jiménez, D. Gómez-Castro
We study well-posedness and long-time behaviour of aggregation-diffusion equations of the form …
Singular solutions for space-time fractional equations in a bounded domain
Hardy Chan, Juan Luis Vázquez, David Gómez-Castro
This paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space operators posed in bounded domai…
Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence
Lucio Boccardo, David Gómez-Castro, Jesús Ildefonso Díaz
In this paper we study existence, uniqueness, and integrability of solutions to the Dirichlet problem in a bounded dom…
Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
Jose A. Carrillo, David Gómez-Castro, Juan Luis Vázquez
We consider density solutions for gradient flow equations of the form , where is the Newtonian repulsive potential in th…