Jesús Ildefonso Díaz Díaz
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View article: Electron beams: partially flat solutions of a nonlinear elliptic equation with a singular absorption term
Electron beams: partially flat solutions of a nonlinear elliptic equation with a singular absorption term Open
In the so-called Child–Langmuir law, established since 1911, an electron beam is formed linking two electrodes, which are assumed to be two parallel plates of area , separated by a finite distance . When , “edge effects” are negl…
View article: Stochastic diffusive energy balance climate model with a multiplicative noise modeling the Solar variability
Stochastic diffusive energy balance climate model with a multiplicative noise modeling the Solar variability Open
We prove the existence, uniqueness, and comparison of solutions for a nonlinear stochastic parabolic partial differential equation that includes the Solar variability in terms of a multiplicative Wiener cylindrical noise in the term of the…
View article: From a small reactive part of the boundary to the whole interior non-reactive domain: critical scale homogenization, optimal control and controllability
From a small reactive part of the boundary to the whole interior non-reactive domain: critical scale homogenization, optimal control and controllability Open
We prove the approximate controllability, for the interior final observation, of the solution of a linear heat equation on $$\Omega \times (0,T)$$ , when the control is placed on a small part of the boundary $$l_{\varepsilon }$$ …
View article: Think globally, act locally: approximate controllability through homogenization of an optimal control problem with control on the boundary of certain particles
Think globally, act locally: approximate controllability through homogenization of an optimal control problem with control on the boundary of certain particles Open
The phrase "Think globally, act locally" became prominent in the context of sustainable development and environmental examples des fonctions activism, encouraging individuals and communities to address global challenges by taking local act…
View article: Title: Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions
Title: Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions Open
We prove the existence of solutions \(u(t,x)\) of the Schrodinger equation with a saturation nonlinear term \((u/|u|)\) having compact support, for each \(t>0\), that expands with a growth law of the type \(C\sqrt{t}\). The primary tool is…
View article: Anisotropic partial symmetrization for some quasilinear equations in comparison with a p-Laplace realization on some of the coordinates
Anisotropic partial symmetrization for some quasilinear equations in comparison with a p-Laplace realization on some of the coordinates Open
View article: A bang-bang optimal control for a nonlinear system modeling the Gate Control Theory of Pain
A bang-bang optimal control for a nonlinear system modeling the Gate Control Theory of Pain Open
We consider a nonlinear system of coupled ordinary differential equations (representing the excitatory, inhibitory, and T-cell potentials) based on the Gate Control Theory of Pain, initially proposed by R. Melzack and P.D. Wall in 1965, an…
View article: A bang-bang optimal control for a nonlinear system modeling the Gate Control Theory of Pain
A bang-bang optimal control for a nonlinear system modeling the Gate Control Theory of Pain Open
View article: Uniqueness and qualitative behavior of solutions to a porous medium equation with Newtonian potential pressure of nonlinear density function
Uniqueness and qualitative behavior of solutions to a porous medium equation with Newtonian potential pressure of nonlinear density function Open
View article: New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles
New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles Open
We pass to the limit in the homogenization of an optimal control problem associated with a parabolic equation with a dynamic boundary condition. New unexpected terms appear due to the critical scale.
View article: Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence
Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence Open
In this article we study the existence, uniqueness, and integrability of solutions to the Dirichlet problem \(-\hbox{div}( M(x) \nabla u ) = -\hbox{div} (E(x) u) + f\) in a bounded domain of \(\mathbb{R}^N\) with \(N \ge 3\). We are partic…
View article: Strange non-local operators homogenizing the Poisson equation with dynamical unilateral boundary conditions: asymmetric particles of critical size
Strange non-local operators homogenizing the Poisson equation with dynamical unilateral boundary conditions: asymmetric particles of critical size Open
We study the homogenization of a nonlinear problem given by the Poisson equation, in a domain with arbitrarily shaped perforations (or particles) and with a dynamic unilateral boundary condition (of Signorini type), with a large coefficien…
View article: On the Compactness of the Support of Solitary Waves of the Complex Saturated Nonlinear Schrödinger Equation and Related Problems
On the Compactness of the Support of Solitary Waves of the Complex Saturated Nonlinear Schrödinger Equation and Related Problems Open
View article: Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions
Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions Open
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term …
View article: Beyond the classical strong maximum principle: forcing changing sign near the boundary and flat solutions
Beyond the classical strong maximum principle: forcing changing sign near the boundary and flat solutions Open
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain $Ω$ can be extended, under suitable conditions, to the case in which the forcing t…
View article: Beyond the classical strong maximum principle: Forcing changing sign near the boundary and flat solutions
Beyond the classical strong maximum principle: Forcing changing sign near the boundary and flat solutions Open
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain $ \Omega $ can be extended, under suitable conditions, to the case in which the fo…
View article: Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity Open
This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr{ö}dinger equation when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law'' $F(|u|^2)u=…
View article: Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence
Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence Open
In this paper we study existence, uniqueness, and integrability of solutions to the Dirichlet problem $-\mathrm{div}( M(x) \nabla u ) = -\mathrm{div} (E(x) u) + f$ in a bounded domain of $\mathbb R^N$ with $N \ge 3$. We are particularly in…
View article: Monotone continuous dependence of solutions of singular quenching parabolic problems
Monotone continuous dependence of solutions of singular quenching parabolic problems Open
We prove the continuous dependence, with respect to the initial datum of solutions of the “quenching parabolic problem” $$\partial _{t}u-\Delta u+\chi _{\{u>0\}}u^{-\beta }=\lambda u^{p}$$ , with zero Dirichlet boundary conditions, when $…
View article: Bottom-up Trust Registry in Self Sovereign Identity
Bottom-up Trust Registry in Self Sovereign Identity Open
Self sovereign identity is a form of decentralised credential management. During credential verification, data exchange only happens between the data owner and the verifier without passing through any third parties. While this approach off…
View article: strange non-local monotone operator arising in the homogenization of a diffusion equation with dynamic nonlinear boundary conditions on particles of critical size and arbitrary shape
strange non-local monotone operator arising in the homogenization of a diffusion equation with dynamic nonlinear boundary conditions on particles of critical size and arbitrary shape Open
We characterize the homogenization limit of the solution of a Poisson equation in a bounded domain, either periodically perforated or containing a set of asymmetric periodical small particles and on the boundaries of these particles a nonl…
View article: Controlled boundary explosions: Dynamics after blow-up for some semilinear problems with global controls
Controlled boundary explosions: Dynamics after blow-up for some semilinear problems with global controls Open
The main goal of this paper is to show that the blow up phenomenon (the explosion of the L ∞-norm) of the solutions of several classes of evolution problems can be controlled by means of suitable global controls α(t) (i.e. only dependent o…
View article: Boundary control and homogenization: Optimal climatization through smart double skin boundaries
Boundary control and homogenization: Optimal climatization through smart double skin boundaries Open
We consider the homogenization of an optimal control problem in which the control $v$ is placed on a part $\Gamma _{0}$ of the boundary and the spatial domain contains a thin layer of “small particles”, very close to the controlling bounda…
View article: Bounded positive solutions for diffusive logistic equations with unbounded distributed limitations
Bounded positive solutions for diffusive logistic equations with unbounded distributed limitations Open
We establish the existence of bounded very weak solutions to a large class of stationary diffusive logistic equations with weights by constructing suitable sub and supersolutions. This class of problems corresponds to the case in which the…
View article: Stochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing
Stochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing Open
We consider a class of one-dimensional nonlinear stochastic parabolic problems associated to Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forcing…
View article: Stochastic energy balance climate models with Legendre weighted diffusion and a cylindrical Wiener process forcing
Stochastic energy balance climate models with Legendre weighted diffusion and a cylindrical Wiener process forcing Open
We consider a class of one-dimensional nonlinear stochastic parabolic problems associated with Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forci…
View article: Stochastic energy balance climate models with Legendre weighted\n diffusion and a cylindrical Wiener process forcing
Stochastic energy balance climate models with Legendre weighted\n diffusion and a cylindrical Wiener process forcing Open
We consider a class of one-dimensional nonlinear stochastic parabolic\nproblems associated with Sellers and Budyko diffusive energy balance climate\nmodels with a Legendre weighted diffusion and an additive cylindrical Wiener\nprocesses fo…
View article: Finite time extinction for a class of damped Schrödinger equations with a singular saturated nonlinearity
Finite time extinction for a class of damped Schrödinger equations with a singular saturated nonlinearity Open
View article: Logarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces
Logarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces Open
We investigate a logarithmically improved regularity criteria in terms of the velocity, for the vorticity, for the Navier-Stokes equations in homogeneous Besov spaces. More precisely, we prove that if the weak solution u satisfies either $…
View article: Steiner symmetrization for anisotropic quasilinear equations \nvia partial discretization
Steiner symmetrization for anisotropic quasilinear equations
\nvia partial discretization Open