11 citations · 41 across the 8 of their papers we have counts for
4 papers · 1 filter
Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart
Gonzalo Galiano, Julián Velasco
We prove that, under a suitable rescaling of the integrable kernel defining the nonlocal diffusion terms, the corresponding sequence of solutions of the Shigesada-Kawasaki-Teramoto…
Well-posedness of a cross-diffusion population model with nonlocal diffusion
Gonzalo Galiano, Julián Velasco
We prove the existence and uniqueness of solution of a nonlocal cross-diffusion competitive population model for two species. The model may be considered as a version, or even an a…
On a cross-diffusion system arising in image denosing
Gonzalo Galiano, Julián Velasco
We study a generalization of a cross-diffusion problem deduced from a nonlinear complex-variable diffusion model for signal and image denoising. We prove the existence of weak solu…
Existence and nonuniqueness of segregated solutions to a class of cross-diffusion systems
Gonzalo Galiano, Sergey Shmarev, Julián Velasco
We study the the Dirichlet problem for the cross-diffusion system \[ \partial_tu_i=\operatorname{div}\left(a_iu_i\nabla (u_1+u_2)\right)+f_i(u_1,u_2),\quad i=1,2,\quad a_i=const>0,…