J. Ignacio Tello
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View article: Depletion of a neural cell adhesion molecule disrupts both epithelial and germ layer identity in sea anemone embryos
Depletion of a neural cell adhesion molecule disrupts both epithelial and germ layer identity in sea anemone embryos Open
Summary Assembly of cells into epithelial layers marks the early steps of tissue organization and embryonic development in most animals. Although several conserved proteins are known to be essential for epithelialization in bilaterians, it…
View article: On a parabolic-elliptic system of chemotaxis with logistic source and non-constant chemotactic coefficient
On a parabolic-elliptic system of chemotaxis with logistic source and non-constant chemotactic coefficient Open
In this article, a parabolic-elliptic system of partial differential equations arising in chemotaxis with non-constant monotone chemotactic sensitivity is analyzed. Let $$\Omega $$ be a bounded and regular domain, u the density of a biol…
View article: A nonlinear elliptic system with a transport term and singular data
A nonlinear elliptic system with a transport term and singular data Open
We consider the nonlinear elliptic system (Formula presented.) where Ω is a bounded, open subset of (Formula presented.), (Formula presented.); (Formula presented.) is a coercive, symmetric matrix with (Formula presented.) coefficients; (F…
View article: A nonlinear elliptic system with transport term and singular data
A nonlinear elliptic system with transport term and singular data Open
We consider the nonlinear elliptic system { u ∈ W 0 N N − 1 ( Ω ): − div ( M ( x ) ∇ u )+ u = − div ( u M ( x ) ∇ ψ )+ f ( x ) , ψ ∈ W 0 1 , 2 ( Ω ): − div ( M ( x ) ∇ ψ )+ ψ = R ( u )+ E ( x ) ∇ ψ , where Ω is a bounded, open subset of R …
View article: On the existence of solutions for a parabolic‐elliptic chemotaxis model with flux limitation and logistic source
On the existence of solutions for a parabolic‐elliptic chemotaxis model with flux limitation and logistic source Open
In this article, we study the existence of solutions of a parabolic‐elliptic system of partial differential equations describing the behaviour of a biological species “ ” and a chemical stimulus “ ” in a bounded and regular domain of . The…
View article: On an elliptic chemotaxis system with flux limitation and subcritical signal production
On an elliptic chemotaxis system with flux limitation and subcritical signal production Open
In this article we study the existence of solutions of a system of partial differential equations of elliptic type, describing the distribution of a biological species "u" and the density of a chemical stimulus "ψ" in a bounded domain Ω of…
View article: Radially symmetric solutions for a Keller-Segel system with flux limitation and nonlinear diffusion
Radially symmetric solutions for a Keller-Segel system with flux limitation and nonlinear diffusion Open
We consider a parabolic-elliptic system of partial differential equations with a chemotactic term in a -dimensional unit ball "" describing the behavior of a biological species "" and a chemical stimuli "". The system presents a sub-linear…
View article: On a comparison method for a parabolic-elliptic system of chemotaxis\n with density-suppressed motility and logistic growth
On a comparison method for a parabolic-elliptic system of chemotaxis\n with density-suppressed motility and logistic growth Open
We consider a parabolic-elliptic system of partial differential equations\nwith chemotaxis and logistic growth given by the system $$ \\left\\{\n\\begin{array}{l} u_t -\\Delta (u \\gamma(v)= \\mu u(1-u), \\\\ - \\Delta v +v=u,\n\\end{array…
View article: On a comparison method for a parabolic-elliptic system of chemotaxis with density-suppressed motility and logistic growth
On a comparison method for a parabolic-elliptic system of chemotaxis with density-suppressed motility and logistic growth Open
We consider a parabolic-elliptic system of partial differential equations with chemotaxis and logistic growth given by the system $$ \left\{ \begin{array}{l} u_t -Δ(u γ(v)= μu(1-u), \\ - Δv +v=u, \end{array} \right. $$ under Neumann bounda…
View article: On a Parabolic-Elliptic system with gradient dependent chemotactic coefficient
On a Parabolic-Elliptic system with gradient dependent chemotactic coefficient Open
We consider a second order PDEs system of Parabolic-Elliptic type with chemotactic terms. The system describes the evolution of a biological species "$u$" moving towards a higher concentration of a chemical stimuli "$v$" in a bounded and o…
View article: Blow up of solutions for a Parabolic-Elliptic Chemotaxis System with\n gradient dependent chemotactic coefficient
Blow up of solutions for a Parabolic-Elliptic Chemotaxis System with\n gradient dependent chemotactic coefficient Open
We consider a Parabolic-Elliptic system of PDE's with a chemotactic term in a\n$N$-dimensional unit ball describing the behavior of the density of a\nbiological species "$u$" and a chemical stimulus "$v$". The system includes a\n nonlinear…
View article: Blow up of solutions for a Parabolic-Elliptic Chemotaxis System with gradient dependent chemotactic coefficient
Blow up of solutions for a Parabolic-Elliptic Chemotaxis System with gradient dependent chemotactic coefficient Open
We consider a Parabolic-Elliptic system of PDE's with a chemotactic term in a $N$-dimensional unit ball describing the behavior of the density of a biological species "$u$" and a chemical stimulus "$v$". The system includes a nonlinear che…
View article: On the Existence of Solutions of a Two-Layer Green Roof Mathematical Model
On the Existence of Solutions of a Two-Layer Green Roof Mathematical Model Open
The aim of this article is to fill part of the existing gap between the mathematical modeling of a green roof and its computational treatment, focusing on the mathematical analysis. We first introduce a two-dimensional mathematical model o…
View article: Complex Ginzburg-Landau equations with a delayed nonlocal perturbation
Complex Ginzburg-Landau equations with a delayed nonlocal perturbation Open
We consider an initial boundary value problem of the complex Ginzburg-Landau equation with some delayed feedback terms proposed for the control of chemical turbulence in reaction diffusion systems. We consider the equation in a bounded dom…
View article: On a Parabolic-ODE system of chemotaxis
On a Parabolic-ODE system of chemotaxis Open
In this article we consider a coupled system of differential equations to describe the evolution of a biological species. The system consists of two equations, a second order parabolic PDE of nonlinear type coupled to an ODE. The system co…
View article: On the number of steady states of a climate energy balance model
On the number of steady states of a climate energy balance model Open
We are concerned with a global climate model with deep ocean effect. The model includes a dynamic and diffusive boundary condition arising from an energy balance on the Earth surface. The scales of time and space are relatively large. One …
View article: On a mathematical model of bone marrow metastatic niche
On a mathematical model of bone marrow metastatic niche Open
We propose a mathematical model to describe tumor cells movement towards a metastasis location into the bone marrow considering the influence of chemotaxis inhibition due to the action of a drug. The model considers the evolution of the si…
View article: Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion
Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion Open
This work studies a general reaction-diffusion model for acid-mediated tumor invasion, where tumor cells produce excess acid that primarily kills healthy cells, and thereby invade the microenvironment. The acid diffuses and could be cleare…
View article: An inverse problem for the compressible Reynolds equation
An inverse problem for the compressible Reynolds equation Open
We study the existence of solutions to a system of equations for equilibrium positions in lubricated journal bearings under load effects. The mechanism under consideration consists of two parallel cylinders, one inside the other, in close …
View article: Enhancing dendritic cell immunotherapy for melanoma using a simple mathematical model
Enhancing dendritic cell immunotherapy for melanoma using a simple mathematical model Open
View article: Numerical resolution of a reinforced random walk model arising in haptotaxis
Numerical resolution of a reinforced random walk model arising in haptotaxis Open