arXiv subjects

Jesus Ildefonso Diaz

Publications and source records attributed to Jesus Ildefonso Diaz.

4 recordsLinked to original sources

arXiv2025

Solutions with expanding compact support of saturated Schr{ö}dinger equations: self-similar solutions

We prove the existence of solutions \(u(t,x)\) of the Schr{ö}dinger 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 considering the self-similar solution of the associated equation. For more information see https://ejde.math.txstate.edu/Volumes/2025/53/abstr.html

math.AP↗

arXiv2025

A bang-bang optimal control for a nonlinear system modeling the Gate Control Theory of Pain

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, and later mathematically modeled by N.F. Britton and S.M. Skevington in 1988.

math.OC↗

arXiv2024

New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles

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.

math.AP↗

arXiv2019

New applications of monotonicity methods to a class of non-monotone parabolic quasilinear sub-homogeneous problems

The main goal of this paper is to show how some monotonicity methods related with the subdifferential of suitable convex functions and its extensions as m-accretive operators in Banach spaces lead to new and unexpected results showing, for instance, the continuous and monotone dependence of solutions with the respect to the data (and coefficients) of the problem. In this way, this paper offers `a common roof' to several methods and results concerning monotone and non-monotone frameworks. Besides to present here some new results, this paper offers also a peculiar survey to some topics which attracted the attention of many specialists in elliptic and parabolic nonlinear partial differential equations in the last years under the important influence of Haim Brezis. To be more precise, the model problem under consideration concerns to positive solutions of a general class of doubly nonlinear diffusion parabolic equations with some sub-homogeneous forcing terms.

math.AP↗