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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.
Boletín de la Sociedad Matemática Mexicana – Springer Journals
Published: Mar 1, 2022
Keywords: Heat sources; Fourier–Bessel series; Maximum deviations; Robust stability; 35A09; 42A16; 34B30; 93D09
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