11 citations · 41 across the 8 of their papers we have counts for
9 papers
Bifurcation in dynamic problems with seasonal succession
Gonzalo Galiano, Julián Velasco
We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, , which determines the…
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…
Well-posedness of a nonlinear integro-differential problem and its rearranged formulation
Gonzalo Galiano, Emanuele Schiavi, Julián Velasco
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the so…
On a fast bilateral filtering formulation using functional rearrangements
Gonzalo Galiano, Julián Velasco
We introduce an exact reformulation of a broad class of neighborhood filters, among which the bilateral filters, in terms of two functional rearrangements: the decreasing and the r…
On a new formulation of nonlocal image filters involving the relative rearrangement
Gonzalo Galiano, Julián Velasco
Nonlocal filters are simple and powerful techniques for image denoising. In this paper we study the reformulation of a broad class of nonlocal filters in terms of two functional re…
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,…
Neighborhood filters and the decreasing rearrangement
Gonzalo Galiano, Julián Velasco
Nonlocal filters are simple and powerful techniques for image denoising. In this paper, we give new insights into the analysis of one kind of them, the Neighborhood filter, by usin…