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 
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/
@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},
     year = {2019},
     number = {12},
     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
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
%U http://geodesic.mathdoc.fr/item/IVM_2019_12_a7/
%G ru
%F 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