Jose Ignacio Tello
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Jose Ignacio Tello has a total of 49 co-authors. Here are the top co-authors by number of shared publications:
- Mihaela Negreanu
Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
10 shared publications - Lourdes Tello
Universidad Politécnica de Madrid
4 shared publications - Antonio Manuel Vargas
Depto. Matemática Aplicada I, UNED, Madrid, Spain
3 shared publications - Dariusz Wrzosek
Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
3 shared publications - Jesús Ildefonso Díaz
Universidad Complutense de Madrid, Instituto de Matemática Interdisciplinar, Plaza de las Ciencias, 3, 28040 Madrid, Spain
3 shared publications - Lucio Boccardo
Istituto Lombardo, Sapienza Università di Roma, Italy
3 shared publications
Latest Publications
- 4 August 2026
- Published by AGH University Press in Opuscula Mathematica
- p. 491
An elliptic system involving p-Laplacian and a chemotactic term
We study the nonlinear elliptic system: \[\begin{cases} u \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla u|^{p-2}\nabla u) + u = -\operatorname{div} (a(x) u|\nabla \psi|^{p-2}\nabla \psi) + f(x), \\ \psi \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla \psi |^{p-2}\nabla \psi) = u^{\theta} \end{cases}\] in a bounded, open subset of \(\mathbb{R}^N\) for \(N \gt 2\) and \(2 \lt p \lt N\), where \(f\) satisfies: \[0 \leq f, \quad f\in L^{(p^*){'}}(\Omega), \quad p^*= \frac{Np}{N-p},\] \(a \in L^{\infty}(\Omega) \) is a given function such that there exist \(\alpha, \beta \in \mathbb{R}\) satisfying \[0\lt\alpha \leq a(x) \leq \beta, \quad x\in \Omega.\] We prove the existence of weak solutions in \([W^{1,p}_0(\Omega)]^2\) under the assumption \[0\lt \theta\lt 1- \frac{2}{p^*}.\]- 4 August 2026
- Published by AGH University Press in Opuscula Mathematica
- p. 491
An elliptic system involving p-Laplacian and a chemotactic term
We study the nonlinear elliptic system: \[\begin{cases} u \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla u|^{p-2}\nabla u) + u = -\operatorname{div} (a(x) u|\nabla \psi|^{p-2}\nabla \psi) + f(x), \\ \psi \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla \psi |^{p-2}\nabla \psi) = u^{\theta} \end{cases}\] in a bounded, open subset of \(\mathbb{R}^N\) for \(N \gt 2\) and \(2 \lt p \lt N\), where \(f\) satisfies: \[0 \leq f, \quad f\in L^{(p^*){'}}(\Omega), \quad p^*= \frac{Np}{N-p},\] \(a \in L^{\infty}(\Omega) \) is a given function such that there exist \(\alpha, \beta \in \mathbb{R}\) satisfying \[0\lt\alpha \leq a(x) \leq \beta, \quad x\in \Omega.\] We prove the existence of weak solutions in \([W^{1,p}_0(\Omega)]^2\) under the assumption \[0\lt \theta\lt 1- \frac{2}{p^*}.\]- 1 May 2026
- Published by Springer Nature
- p. 153-165
Mathematical Aspects of Parabolic-Elliptic Chemotactic Systems with Flux Limitation
- 1 May 2026
- Published by Springer Nature
- p. 153-165
Mathematical Aspects of Parabolic-Elliptic Chemotactic Systems with Flux Limitation
- Open Access
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 11 (8) , 25839-25860
On a chemorepulsion elliptic system with nonlinear production and weak data
Let $ \Omega $ be a bounded Lipschitz domain in $ {\mathbb{R}}^N $, with $ N \geq 3 $ and $ \chi > 0 $. Let $ M(x) $ be a symmetric positive definite matrix with coefficients $ m_{ij} \in L^{\infty} (\Omega) $. We study the problem: $ \left\{ \begin{array}{ll} - \mbox{div}(M(x) \nabla u) + u = \chi \mbox{div}(uM(x) \, \nabla \psi ) + f(x), \\ - \mbox{div}(M(x) \nabla \psi) +\psi = u^{\theta}+g(x). \end{array} \right. $ Under the assumptions $ 1. $ $ \theta < \frac{N+2}{N-2} $; $ 2. $ $ f \geq 0 $, $ f \in L^{m}(\Omega) $, for $ m > \frac{2N}{N+2} $; $ 3. $ $ g \geq 0 $, $ g \in L^{q}(\Omega) $, for $ q > \frac{2N}{N+2} $, we prove the existence of at least one weak solution in $ W^{1, \frac{N}{N-1}} (\Omega) \times W^{1, 2} (\Omega) $. Moreover, under the assumptions $ 4. $ $ \theta < \frac{2}{N-2} $; $ 5. $ $ g \in L^{q}(\Omega) \mbox{ for some }q > \frac{N}{2}, $ we have $ u \in W^{1, 2} (\Omega), \quad \psi \in W^{1, 2} (\Omega) \cap L^{\infty}(\Omega). $- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 11 (8) , 25839-25860
Open AccessOn a chemorepulsion elliptic system with nonlinear production and weak data
Let $ \Omega $ be a bounded Lipschitz domain in $ {\mathbb{R}}^N $, with $ N \geq 3 $ and $ \chi > 0 $. Let $ M(x) $ be a symmetric positive definite matrix with coefficients $ m_{ij} \in L^{\infty} (\Omega) $. We study the problem: $ \left\{ \begin{array}{ll} - \mbox{div}(M(x) \nabla u) + u = \chi \mbox{div}(uM(x) \, \nabla \psi ) + f(x), \\ - \mbox{div}(M(x) \nabla \psi) +\psi = u^{\theta}+g(x). \end{array} \right. $ Under the assumptions $ 1. $ $ \theta < \frac{N+2}{N-2} $; $ 2. $ $ f \geq 0 $, $ f \in L^{m}(\Omega) $, for $ m > \frac{2N}{N+2} $; $ 3. $ $ g \geq 0 $, $ g \in L^{q}(\Omega) $, for $ q > \frac{2N}{N+2} $, we prove the existence of at least one weak solution in $ W^{1, \frac{N}{N-1}} (\Omega) \times W^{1, 2} (\Omega) $. Moreover, under the assumptions $ 4. $ $ \theta < \frac{2}{N-2} $; $ 5. $ $ g \in L^{q}(\Omega) \mbox{ for some }q > \frac{N}{2}, $ we have $ u \in W^{1, 2} (\Omega), \quad \psi \in W^{1, 2} (\Omega) \cap L^{\infty}(\Omega). $ - 1 January 2026
- Published by AGH University Press in Opuscula Mathematica
- p. 491-511
An elliptic system involving p-Laplacian and a chemotactic term
We study the nonlinear elliptic system: \[\begin{cases} u \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla u|^{p-2}\nabla u) + u = -\operatorname{div} (a(x) u|\nabla \psi|^{p-2}\nabla \psi) + f(x), \\ \psi \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla \psi |^{p-2}\nabla \psi) = u^{\theta} \end{cases}\] in a bounded, open subset of \(\mathbb{R}^N\) for \(N \gt 2\) and \(2 \lt p \lt N\), where \(f\) satisfies: \[0 \leq f, \quad f\in L^{(p^*){'}}(\Omega), \quad p^*= \frac{Np}{N-p},\] \(a \in L^{\infty}(\Omega) \) is a given function such that there exist \(\alpha, \beta \in \mathbb{R}\) satisfying \[0\lt\alpha \leq a(x) \leq \beta, \quad x\in \Omega.\] We prove the existence of weak solutions in \([W^{1,p}_0(\Omega)]^2\) under the assumption \[0\lt \theta\lt 1- \frac{2}{p^*}.\]- 1 January 2026
- Published by AGH University Press in Opuscula Mathematica
- p. 491-511
An elliptic system involving p-Laplacian and a chemotactic term
We study the nonlinear elliptic system: \[\begin{cases} u \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla u|^{p-2}\nabla u) + u = -\operatorname{div} (a(x) u|\nabla \psi|^{p-2}\nabla \psi) + f(x), \\ \psi \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla \psi |^{p-2}\nabla \psi) = u^{\theta} \end{cases}\] in a bounded, open subset of \(\mathbb{R}^N\) for \(N \gt 2\) and \(2 \lt p \lt N\), where \(f\) satisfies: \[0 \leq f, \quad f\in L^{(p^*){'}}(\Omega), \quad p^*= \frac{Np}{N-p},\] \(a \in L^{\infty}(\Omega) \) is a given function such that there exist \(\alpha, \beta \in \mathbb{R}\) satisfying \[0\lt\alpha \leq a(x) \leq \beta, \quad x\in \Omega.\] We prove the existence of weak solutions in \([W^{1,p}_0(\Omega)]^2\) under the assumption \[0\lt \theta\lt 1- \frac{2}{p^*}.\]- 14 November 2025
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 36 (01) , 173-204
From indirect to direct taxis by fast reaction limit
Many population models formulated in terms of quasi-linear parabolic systems incorporate taxis, understood as directed movement of animals in response to some stimulus. Taxis is called direct if the animals follow the density gradient of another population, or indirect if they follow the density of a chemical secreted by individuals from another population. We prove that in the so-called fast reaction limit, i.e. when the ratio [ ] of the chemical signal diffusion to the signal production/degradation vanishes asymptotically, the solution of the model with indirect taxis converges to the solution of the model with direct taxis. It is justified then to replace the gradient of the chemical by the gradient in population density, reducing by one the number of equations in the indirect taxis model. The kinetic part of the considered models describes competition or predation, and the taxis term refers to the avoidance strategy assigned to one of the competitors or to a prey-taxis. Under certain compatibility condition satisfied by the initial data for the space dimension [ ], convergence occurs in a strong topology of function spaces, and its rate can be controlled by [ ]. Otherwise, the compactness argument only leads to convergence for a subsequence in the appropriate weak sense.
- 14 November 2025
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 36 (01) , 173-204
From indirect to direct taxis by fast reaction limit
Many population models formulated in terms of quasi-linear parabolic systems incorporate taxis, understood as directed movement of animals in response to some stimulus. Taxis is called direct if the animals follow the density gradient of another population, or indirect if they follow the density of a chemical secreted by individuals from another population. We prove that in the so-called fast reaction limit, i.e. when the ratio [ ] of the chemical signal diffusion to the signal production/degradation vanishes asymptotically, the solution of the model with indirect taxis converges to the solution of the model with direct taxis. It is justified then to replace the gradient of the chemical by the gradient in population density, reducing by one the number of equations in the indirect taxis model. The kinetic part of the considered models describes competition or predation, and the taxis term refers to the avoidance strategy assigned to one of the competitors or to a prey-taxis. Under certain compatibility condition satisfied by the initial data for the space dimension [ ], convergence occurs in a strong topology of function spaces, and its rate can be controlled by [ ]. Otherwise, the compactness argument only leads to convergence for a subsequence in the appropriate weak sense.
- Open Access
- 6 May 2025
- Published by Springer Nature in Journal of Elliptic and Parabolic Equations
- Vol. 11 (3) , 2219-2240
On a parabolic-elliptic system of chemotaxis with logistic source and non-constant chemotactic coefficient
- 6 May 2025
- Published by Springer Nature in Journal of Elliptic and Parabolic Equations
- Vol. 11 (3) , 2219-2240
Open AccessOn a parabolic-elliptic system of chemotaxis with logistic source and non-constant chemotactic coefficient
- Open Access
On the existence of solutions for a parabolic-elliptic chemotaxis model with flux limitation and logistic source
In this paper we study the existence of solutions of a parabolic-elliptic system of partial differential equations describing the behaviour of a biological species $u$ and a chemical stimulus $v$ in a bounded and regular domain $Ω$ of $\mathbb{R}^N$. The equation for $u$ is a parabolic equation with a nonlinear second order term of chemotaxis type with flux limitation as $ -χdiv (u |\nabla ψ|^{p-2} \nabla v)$, for $p>1$. The chemical substance distribution $v$ satisfies the elliptic equation $-Δv+v=u$. The evolution of $u$ is also determined by a logistic type growth term $μu(1-u)$. The system is studied under homogeneous Neumann boundary conditions. The main result of the article is the existence of uniformly bounded solutions for $p<3/2$ and any $N\ge 2$.Open AccessOn the existence of solutions for a parabolic-elliptic chemotaxis model with flux limitation and logistic source
In this paper we study the existence of solutions of a parabolic-elliptic system of partial differential equations describing the behaviour of a biological species $u$ and a chemical stimulus $v$ in a bounded and regular domain $Ω$ of $\mathbb{R}^N$. The equation for $u$ is a parabolic equation with a nonlinear second order term of chemotaxis type with flux limitation as $ -χdiv (u |\nabla ψ|^{p-2} \nabla v)$, for $p>1$. The chemical substance distribution $v$ satisfies the elliptic equation $-Δv+v=u$. The evolution of $u$ is also determined by a logistic type growth term $μu(1-u)$. The system is studied under homogeneous Neumann boundary conditions. The main result of the article is the existence of uniformly bounded solutions for $p<3/2$ and any $N\ge 2$. - 7 March 2024
- Published by Taylor & Francis in Applicable Analysis
- Vol. 103 (16) , 2893-2908
A nonlinear elliptic system with a transport term and singular data
1. In this paper we study the nonlinear elliptic system (1) {0≤u∈W0NN−1(Ω):−div(M(x)∇u)+u=−div(uM(x)∇ψ)+f(x),0≤ψ∈W01,2(Ω):−div(M(x)∇ψ)+ψ=R(u)+E(x)∇ψ, under the following assumptions. Ω is a bounded...
- 7 March 2024
- Published by Taylor & Francis in Applicable Analysis
- Vol. 103 (16) , 2893-2908
A nonlinear elliptic system with a transport term and singular data
1. In this paper we study the nonlinear elliptic system (1) {0≤u∈W0NN−1(Ω):−div(M(x)∇u)+u=−div(uM(x)∇ψ)+f(x),0≤ψ∈W01,2(Ω):−div(M(x)∇ψ)+ψ=R(u)+E(x)∇ψ, under the following assumptions. Ω is a bounded...
- Open Access
- 30 September 2023
- Published by Wiley
A nonlinear elliptic system with transport term and singular data
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 N , N≥3 ; M( x) is a coercive, symmetric matrix with L ∞ ( Ω ) coefficients; f( x) and E( x) belong to some Lebesgue space, and R( s) is a continuous function such that 0 ≤ R ( s ) ≤ | s | θ , for θ < 2 N . Using a duality technique, we prove existence of at least a weak solution ( u,ψ) . Moreover, if N=3 or N=4 , we prove under stronger assumptions on f( x) and E( x) that the solution u belongs to W 0 1 , 2 ( Ω ) .
- 30 September 2023
- Published by Wiley
Open AccessA nonlinear elliptic system with transport term and singular data
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 N , N≥3 ; M( x) is a coercive, symmetric matrix with L ∞ ( Ω ) coefficients; f( x) and E( x) belong to some Lebesgue space, and R( s) is a continuous function such that 0 ≤ R ( s ) ≤ | s | θ , for θ < 2 N . Using a duality technique, we prove existence of at least a weak solution ( u,ψ) . Moreover, if N=3 or N=4 , we prove under stronger assumptions on f( x) and E( x) that the solution u belongs to W 0 1 , 2 ( Ω ) .
- 2 August 2023
- Published by Springer Nature in Zeitschrift für angewandte Mathematik und Physik
- Vol. 74 (5) , 1-15
A nonlinear elliptic system with a transport term and singular data
- 2 August 2023
- Published by Springer Nature in Zeitschrift für angewandte Mathematik und Physik
- Vol. 74 (5) , 1-15
A nonlinear elliptic system with a transport term and singular data