Modification of the Dynamic Regularization Method for Linear Parabolic Equations

We consider the problem of reconstructing distributed inputs (disturbances) in linear parabolic equations. An algorithm for solving this problem is given. An upper bound for the convergence rate is established for the case in which the input is a function of bounded variation. The algorithm combines...

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Bibliographic Details
Published in:Differential equations 2020-11, Vol.56 (11), p.1452-1462
Main Author: Maksimov, V. I.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Control Theory
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Methods
Ordinary Differential Equations
Partial Differential Equations
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Summary:We consider the problem of reconstructing distributed inputs (disturbances) in linear parabolic equations. An algorithm for solving this problem is given. An upper bound for the convergence rate is established for the case in which the input is a function of bounded variation. The algorithm combines the optimal preset and positional control methods and permits reconstruction based on inaccurate measurements of solutions of the equations at discrete time instants.
ISSN:0012-2661
1608-3083
DOI:10.1134/S00122661200110063