4 citations · 8 across the 14 of their papers we have counts for
16 papers
Modeling of an ODE-constrained optimization problem describing tumor dynamics, and numerical approximation via sequential physics-informed neural networks
Juan J. Forero-Hernández, Élder J. Villamizar-Roa
In this paper, we study an optimal control problem related to an ODE model of glioblastoma growth influenced by the oxygen. The model considers a couple of controls describing the…
Optimal Bilinear control restricted to the three-dimensional chemo-repulsion model with potential production
Francisco Guillen-Gonzalez, Exequiel Mallea-Zepeda, Maria A. Rodriguez-Bellido +1
In this paper we study the following three-dimensional parabolic-parabolic chemo-repulsion model with potential production, logistic reaction and bilinear control, defined in $Q=(0…
On the fractional heat semigroup and product estimates in Besov spaces and applications in theoretical analysis of the fractional Keller-Segel system
Jhean E. Pérez-López, Diego A. Rueda-Gómez, Élder J. Villamizar-Roa
This paper is concerned with the fractional Keller-Segel system in the temporal and spatial variables. We consider fractional dissipation for the physical variables including a fra…
Theoretical and numerical analysis for an interspecies competition model with chemoattraction-consumption in fluids
Carlos Mateo Beltrán-Larrotta, Diego Armando Rueda-Gómez, Élder Jesús Villamizar-Roa
This work is devoted to the theoretical and numerical analysis of a two-species chemotaxis- Navier-Stokes system with Lotka-Volterra competitive kinetics in a bounded domain of Rd,…
Existence theory of the nonlinear plate equations
Carlos Banquet, Gilmar Garbugio, Élder J. Villamizar-Roa
This paper is devoted to the theoretical analysis of the nonlinear plate equations in with nonlinearity involving a type polynomial beh…
Convergence and positivity of finite element methods for a haptotaxis model of tumoral invasion
Viviana Niño-Celis, Diego Armando Rueda-Gómez, Élder Jesús Villamizar Roa
In this paper, we consider a mathematical model for the invasion of host tissue by tumour cells in a -dimensional bounded domain, . This model consists of a system of d…
On a bi-dimensional chemo-repulsion model with nonlinear production
Francisco Guillén-González, Exequiel Mallea-Zepeda, Élder J. Villamizar-Roa
In this paper, we study the following parabolic chemo-repulsion with nonlinear production model: $$ \left\{ \begin{array}{rcl} \partial_tu-Δu&=&\nabla\cdot(u\nabla v),\\ \partial_t…
Numerical analysis for a chemotaxis-Navier-Stokes system
Abelardo Duarte-Rodríguez, María A. Rodríguez-Bellido, Diego A. Rueda-Gómez +1
In this paper we develop a numerical scheme for approximating a -dimensional chemotaxis-Navier-Stokes system, , modeling cellular swimming in incompressible fluids. This…
An optimal control problem for the Navier-Stokes- system
Exequiel Mallea-Zepeda, Elva Ortega-Torres, Élder J. Villamizar-Roa
In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes- model. We prove the solvability of the optimal control problem, and derive fi…
Existence theory for the Boussinesq equation in Modulation spaces
Élder J. Villamizar-Roa, Carlos Banquet Brango
In this paper we study the Cauchy problem for the generalized Boussinesq equation with initial data in modulation spaces After a deco…
An Optimal Control Problem for the Steady Nonhomogeneous Asymmetric Fluids
Exequiel Mallea-Zepeda, Elva Ortega-Torres, Élder J. Villamizar-Roa
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary contro…
A boundary control problem associated to the Rayleigh-Bénard-Marangoni system
Elder J. Villamizar-Roa, Diego A. Rueda-Gómez
In this paper, we study a boundary control problem associated to the stationary Rayleigh-Bénard-Marangoni (RBM) system in presence of controls for the velocity and the temperature…
On the Schrödinger equations with isotropic and anisotropic fourth-order dispersion
Carlos Banquet, Elder J. Villamizar-Roa
This paper deals with the Cauchy problem associated to the nonlinear fourth-order Schrödinger equation with isotropic and anisotropic mixed dispersion. This model is given by the e…
A Distributed Control Problem for a Three-Dimensional Lagrangian Averaged Navier-Stiokes-α MODEL
Elder J. Villamizar-Roa, Elva Ortega-Torres
A distributed optimal control problem with final observation for a three- dimensional Lagrange averaged Navier-Stokes-? model is studied. The solvability of the optimal control pro…
On the non-homogeneous Navier-Stokes system with Navier friction boundary conditions
Lucas C. F. Ferreira, Gabriela Planas, Elder J. Villamizar-Roa
We address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and…
On the existence of infinite energy solutions for nonlinear Schrodinger equations
P. Braz e Silva, L. C. F. Ferreira, E. J. Villamizar-Roa
We derive new results about existence and uniqueness of local and global solutions for nonlinear Schrodinger equation, including self-similar global solutions. Our analysis is perf…