Control of Semilinear Differential Equations with Moving Singularities

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...

Full description

Saved in:
Bibliographic Details
Published in:Fractal and fractional Vol. 9; no. 4; p. 198
Main Authors: Precup, Radu, Stan, Andrei, Du, Wei-Shih
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.04.2025
Subjects:
Algorithms
bisection algorithm
control problem
Controllability
differential equation
Differential equations
Fractional calculus
fractional differential equation
Guarantees
lower and upper solutions
moving singularity
Numerical analysis
Parameters
Physics
Singularities
United States
Romania
ISSN:2504-3110, 2504-3110
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract9040198