44 citations · 96 across the 17 of their papers we have counts for
18 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…
Symmetrization in nonlocal diffusion problems
Gonzalo Galiano
We study Talenti's type symmetrization properties for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution…
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…
Error analysis of some nonlocal diffusion discretization schemes
Gonzalo Galiano
We study two numerical approximations of solutions of nonlocal diffusion evolution problems which are inspired in algorithms for computing the bilateral denoising filtering of an i…
Turing instability analysis of a singular cross-diffusion problem
Gonzalo Galiano, Víctor González-Tabernero
The population model of Busenberg and Travis is a paradigmatic model in ecology and tumour modelling due to its ability to capture interesting phenomena like the segregation of pop…
An economic cross-diffusion mutualistic model for cities emergence
Gonzalo F. de-Córdoba, Gonzalo Galiano
We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic beh…
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…
Non-convex non-local flows for saliency detection
Iván Ramírez, Gonzalo Galiano, Emanuele Schiavi
We propose and numerically solve a new variational model for automatic saliency detection in digital images. Using a non-local framework we consider a family of edge preserving fun…
Well-posedness of an evolution problem with nonlocal diffusion
Gonzalo Galiano
We prove the well-posedness of a general evolution reaction-nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continu…
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…
Analysis of a splitting-differentiation population model leading to cross-diffusion
Gonzalo Galiano, Virginia Selgas
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single sp…
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 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…
On a cross-diffusion segregation problem arising from a model of interacting particles
Gonzalo Galiano, Virginia Selgas
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by t…
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,…
Deterministic particle method approximation of a contact inhibition cross-diffusion problem
Gonzalo Galiano, Virginia Selgas
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of…
On a singular perturbation problem arising in the theory of Evolutionary Distributions
Gonzalo Galiano, Yosef Cohen
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection…
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…