Boundary control associated with a parabolic equation
Volume 33, Issue 2, pp 146--154
https://dx.doi.org/10.22436/jmcs.033.02.03
Publication Date: December 05, 2023
Submission Date: January 11, 2023
Revision Date: September 28, 2023
Accteptance Date: November 01, 2023
Authors
F. N. Dekhkonov
- Department of Mathematics, Namangan State University, Uychi street 316, 160136 Namangan, Uzbekistan.
- Department of Mathematics, New Uzbekistan University, Mustaqillik Ave. 54, 100007 Tashkent, Uzbekistan.
Abstract
In this paper, we consider a boundary control problem associated with a parabolic equation. On the part of the border of the considered domain, the value of the solution with control parameter is given. Restrictions on the control are given in such a way that the average value of the solution in some part of the considered domain gets a given value. The auxiliary problem is solved by the method of separation of variables, while the problem in consideration is reduced to the Volterra integral equation. By Laplace transform method, the existence theorem for admissible control is proved.
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ISRP Style
F. N. Dekhkonov, Boundary control associated with a parabolic equation, Journal of Mathematics and Computer Science, 33 (2024), no. 2, 146--154
AMA Style
Dekhkonov F. N., Boundary control associated with a parabolic equation. J Math Comput SCI-JM. (2024); 33(2):146--154
Chicago/Turabian Style
Dekhkonov, F. N.. "Boundary control associated with a parabolic equation." Journal of Mathematics and Computer Science, 33, no. 2 (2024): 146--154
Keywords
- Parabolic equation
- integral equation
- initial-boundary value problem
- admissible control
MSC
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