On a Robust Stability Criterion of the Radially Symmetric Heat Equation

This paper establishes a robust stability criterion in the radially symmetric heat equation that admits heat sources belonging to a set of bounded functions. The robust stability criterion is determined by extending a definition of stability under constant-acting perturbations that was originally es...

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Bibliographic Details
Published inJournal of dynamical and control systems Vol. 30; no. 3
Main Author Temoltzi-Ávila, R.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2024
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Control
Differential equations
Dynamical Systems
Dynamical Systems and Ergodic Theory
Fourier series
Heat sources
Mathematics
Mathematics and Statistics
Robustness (mathematics)
Stability criteria
Systems Theory
Thermodynamics
Vibration
Heat sources
Robust stability
93D09
Reachability tube
34B30
Fourier series
42A16
35A09
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Summary:This paper establishes a robust stability criterion in the radially symmetric heat equation that admits heat sources belonging to a set of bounded functions. The robust stability criterion is determined by extending a definition of stability under constant-acting perturbations that was originally established for systems of ordinary differential equations. It is assumed that heat sources admit a Fourier series representation whose coefficients are bounded and piecewise continuous functions. The robust stability criterion obtained is useful to conclude that the solution of the heat equation, as well as its first partial derivatives with respect to the radial axis and with respect to time, are bounded by a constant whose value is initially established. The results obtained are illustrated numerically.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-024-09701-4