Work

Control of Semilinear Differential Equations with Moving Singularities

Year: 2025

Type: article

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 techniques 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.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9040198

Authors: Radu Precup, Andrei Stan, Wei-Shih Du

Institutions: Babeș-Bolyai University, Tiberiu Popoviciu Institute of Numerical Analysis, National Kaohsiung Normal University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: National Science and Technology Council