Geodesic
Boundary control of the heat transfer process in the space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2019), pp. 82-90.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the simplest mathematical model of the following problem. On the part of the border of region $D\subset {\mathbb R}^{2}$ there is a heater having an adjustable temperature. It is required to find such a mode of operation of the heater so that the average temperature in a certain subregion of region $D$ takes the specified value. The existence of the control parameter proved under certain restrictions on the values of the function defined by the integral constraint.
Mots-clés : parabolic equation, Laplace transform.
Keywords: boundary value problem, control problem, control parameter, first kind Volterra integral equation 
@article{IVM_2019_12_a7,
     author = {Z. K. Fayazova},
     title = {Boundary control of the heat transfer process in the space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {82--90},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_12_a7/}
}
TY  - JOUR
AU  - Z. K. Fayazova
TI  - Boundary control of the heat transfer process in the space
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 82
EP  - 90
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2019_12_a7/
LA  - ru
ID  - IVM_2019_12_a7
ER  - 
%0 Journal Article
%A Z. K. Fayazova
%T Boundary control of the heat transfer process in the space
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 82-90
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2019_12_a7/
%G ru
%F IVM_2019_12_a7
Z. K. Fayazova. Boundary control of the heat transfer process in the space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2019), pp. 82-90. http://geodesic.mathdoc.fr/item/IVM_2019_12_a7/

[1] White L. W., “Point control: approximations of parabolic problems and pseudo parabolic problems”, Appl. Anal., 12:4 (1981), 251–263 | DOI | MR | Zbl

[2] Lyashko S. I., “O razreshimosti psevdo-parabolicheskikh uravnenii”, Izv. vuzov. Matem., 1985, no. 9, 71–72

[3] Lyashko S. I., Mankovskii A. A., “Optimalnoe impulsnoe upravlenie sistemoi s raspredelennymi parametrami giperbolicheskogo tipa”, DAN USSR, 1983, no. 4, 69–71 | Zbl

[4] Lyashko S. I., Mankovskii A. A., “Odnovremennaya optimizatsiya momentov i intensivnostei impulsov v zadachakh upravleniya dlya parabolicheskikh uravnenii”, Kibernetika, 87:3 (1983), 81–82

[5] Fursikov A. V., Optimal control of distributed systems: Theory and Appl., Translations of Math. Monograpfs, 187, Amer. Math. Soc., Providence, 2000 | MR

[6] Ilin V. A., “Granichnoe upravlenie protsessom kolebanii na odnom kontse pri zakreplennom vtorom kontse v terminakh obobschennogo resheniya volnovogo uravneniya s konechnoi energiei”, Differents. uravneniya, 36:12 (2000), 1670–1686 | Zbl

[7] Ilin V. A., Moiseev E. I., “Optimizatsiya granichnykh upravlenii kolebaniyami struny”, UMN, 60:6 (2005), 89–114 | DOI | MR | Zbl

[8] Albeverio S., Alimov Sh., “On a time-optimal control problem associated with the heat exchange process”, Appl. Math. and Optim., 57:1 (2008), 58–68 | DOI | MR | Zbl

[9] Barbu V., “The time-optimal control problem for parabolic variational inequalities”, App. Math. Optim., 11:1 (1984), 1–22 | DOI | MR

[10] Barbu V., Răşcanu A., Tessitore G., “Carleman estimates and controllability of linear stochastic heat equations”, Appl. Math. Optim., 47:2 (2003), 97–120 | DOI | MR | Zbl

[11] Fattorini H. O., “Time-optimal control of solutions of operational differential equations”, SIAM J. Control Ser. A, 2 (1964), 54–59 | MR | Zbl

[12] Fattorini H. O., “Time and norm optimal control for linear parabolic equations: nessesary and suffisient conditions”, Control and Estimation of Distributed Parameter Systems, Internat. Ser. of Numerical Math., 143, Birkhäuser, Basel, 2002, 151–168

[13] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967