The boundary control problem for heat equation in a right rectangle domain is considered. The control parameter is equal to the temperature on some part of the border of the considered domain The estimate of a minimal time for achieving the given average temperature over some subdomain is found.
1. Alimov Sh.A. On a control problem associated with the heat transfer process. Eurasian Mathematical Journal, No. 1, 17–30 (2010).
2. Albeverio S., Alimov Sh.A. On one time-optimal control problem associated with the heat exchange process. Applied Mathematics and Optimization, Vol. 47, No. 1, 58–68 (2008).
3. Alimov Sh.A., Dekhkonov F.N. On the time-optimal control of the heat exchange process. Uzbek Mathematical Journal, No. 2, 4–17 (2019).
4. Alimov Sh.A. On the null-controllability of the heat exchange process. Eurasian Mathematical Journal, No. 2, 5–19 (2011).
5. Alimov Sh. A., Dekhkonov F.N. On a control problem associated with fast heating of a thin rod, Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences, Vol. 2, Iss. 1, Article 1, (2019).
6. Fattorini H.O. Time-Optimal control of solutions of operational differential equations, SIAM J. Control, Vol. 2, 49–65 (1964).
7. Fattorini H.O. Time and norm optimal control for linear parabolic equations: necessary and sufficient conditions, Control and Estimation of Distributed Parameter Systems, International Series of Numerical Mathematics, Vol. 126, 151–168 (2002).
8. Barbu V. The time-optimal control problem for parabolic variotianal inequalities, Applied Mathematics and Optimization, Vol. 11, 1–22 (1984).
9. Friedman A. Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, XVI, (1964).
10. Fursikov A.V. Optimal Control of Distributed Systems, Theory and Applications, Translations of Math. Monographs, 187, Amer. Math. Soc., (2000).
11. Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N. Linear and Quasi-Linear Equations of Parabolic Type (Russian). Nauka, Moscow, (1967).
12. Fayazova Z.K. Boundary control of the heat transfer process in the space, Izv. Vyssh. Ucheben. Zaved. Mat., No. 12, 82–90 (2019).
13. Altmüller A., Grüne L. Distributed and boundary model predictive control for the heat equation. Technical report, University of Bayreuth, Department of Mathematics, (2012).
14. Lions J.L. Contróle optimal de systèmes gouvernés par des équations aux dérivées partielles. Dunod Gauthier-Villars, Paris, (1968).
15. Fayazova Z.K. Boundary control for a Psevdo-Parabolic equation, Mathematical notes of NEFU, Vol. 25, No. 2, 40–45 (2018).
16. Tukhtasinov M., Mustapokulov Kh., Ibragimov G. Invariant Constant Multi-Valued Mapping for the Heat Conductivity Proplem. Malasian Journal of Mathematical Sciences, Vol. 13, No. 1, 61–74 (2019).
17. Tikhonov A.N., Samarsky A.A. Equations of Mathematical Physics, Nauka, Moscow, (1966).
18. Vladimirov V.S. Equations of Mathematical Physics, Marcel Dekker, New York, (1971).
"On time-optimal control problem associated with parabolic equation,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 4
, Article 5.
Available at: https://uzjournals.edu.uz/mns_nuu/vol4/iss1/5