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...

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Vydáno v:Fractal and fractional Ročník 9; číslo 4; s. 198
Hlavní autoři: Precup, Radu, Stan, Andrei, Du, Wei-Shih
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.04.2025
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract9040198