Control of semilinear differential equations with moving singularities
Optimization and Control
2025-05-20 v1
Abstract
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact that it depends on the singular point which in turn depends on the control variable. We provide sufficient conditions to ensure that the functional determining the control is continuous over the entire domain of the parameter. Lower and upper solutions technique combined with a bisection algorithm is used to prove the controllability of the equation and to approximate the control. An example is given together with some numerical simulations. The results naturally extend to fractional differential equations.
Cite
@article{arxiv.2505.11531,
title = {Control of semilinear differential equations with moving singularities},
author = {Radu Precup and Andrei Stan and Wei-Shih Du},
journal= {arXiv preprint arXiv:2505.11531},
year = {2025}
}