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Robust stability of the heat equation on a radial symmetric plate

Robust stability of the heat equation on a radial symmetric plate An non-homogeneous heat equation in the presence of an external uncertain perturbation is considered. We investigated the problem of finding solutions with the possible maximum amplitude, by employing the Fourier–Bessel method of separation of variables and the maximum deviation problem of solutions of first-order differential equations with external uncertain perturbations. The application of the Fourier–Bessel method is justified by the existence of solutions of the heat equation under the influence of heat sources that belong to an initially prescribed set. The robust stability property of the solutions of the heat equation is investigated using the robust stability of the Fourier–Bessel coefficients; in particular, the properties of the reachability tubes of the Fourier–Bessel coefficients are defined in a finite time interval. The robust stability criterion obtained for the radially symmetric heat equation is actually a generalization of a robust stability concept commonly considered in ordinary differential equations. The results obtained are illustrated numerically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Boletín de la Sociedad Matemática Mexicana Springer Journals

Robust stability of the heat equation on a radial symmetric plate

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References (13)

Publisher
Springer Journals
Copyright
Copyright © Sociedad Matemática Mexicana 2022
ISSN
1405-213X
eISSN
2296-4495
DOI
10.1007/s40590-021-00405-4
Publisher site
See Article on Publisher Site

Abstract

An non-homogeneous heat equation in the presence of an external uncertain perturbation is considered. We investigated the problem of finding solutions with the possible maximum amplitude, by employing the Fourier–Bessel method of separation of variables and the maximum deviation problem of solutions of first-order differential equations with external uncertain perturbations. The application of the Fourier–Bessel method is justified by the existence of solutions of the heat equation under the influence of heat sources that belong to an initially prescribed set. The robust stability property of the solutions of the heat equation is investigated using the robust stability of the Fourier–Bessel coefficients; in particular, the properties of the reachability tubes of the Fourier–Bessel coefficients are defined in a finite time interval. The robust stability criterion obtained for the radially symmetric heat equation is actually a generalization of a robust stability concept commonly considered in ordinary differential equations. The results obtained are illustrated numerically.

Journal

Boletín de la Sociedad Matemática MexicanaSpringer Journals

Published: Mar 1, 2022

Keywords: Heat sources; Fourier–Bessel series; Maximum deviations; Robust stability; 35A09; 42A16; 34B30; 93D09

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