Abstract:
We consider the simplest mathematical model of the following problem.
On the part of the border of region D⊂R2 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.
Keywords:
parabolic equation, boundary value problem, control problem, control parameter, first kind Volterra integral equation, Laplace transform.
Citation:
Z. K. Fayazova, “Boundary control of the heat transfer process in the space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 12, 82–90; Russian Math. (Iz. VUZ), 63:12 (2019), 71–79
\Bibitem{Fay19}
\by Z.~K.~Fayazova
\paper Boundary control of the heat transfer process in the space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2019
\issue 12
\pages 82--90
\mathnet{http://mi.mathnet.ru/ivm9529}
\crossref{https://doi.org/10.26907/0021-3446-2019-12-82-90}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2019
\vol 63
\issue 12
\pages 71--79
\crossref{https://doi.org/10.3103/S1066369X19120089}
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Linking options:
https://www.mathnet.ru/eng/ivm9529
https://www.mathnet.ru/eng/ivm/y2019/i12/p82
This publication is cited in the following 10 articles:
Farrukh Dekhkonov, Wenke Li, “On the boundary control problem associated with a fourth order parabolic equation in a two-dimensional domain”, DCDS-S, 2024
F. N. Dekhkonov, “The control problem for a heat conduction equation with Neumann boundary condition”, Vestnik KRAUNTs. Fiz.-mat. nauki, 47:2 (2024), 9–20
F. N. Dekhkonov, “On the boundary control problem for a pseudo-parabolic equation with involution”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 20:3 (2024), 416–427
F. N. Dekhkonov, “Control problem concerned with the process of heating a thin plate”, Vestnik KRAUNTs. Fiz.-mat. nauki, 42:1 (2023), 69–79
K. V. Perevozchikova, N. A. Manakova, “Investigation of boundary control and final observation in mathematical model of motion speed potentials distribution of filtered liquid free surface”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:2 (2023), 111–116
Farrukh Dekhkonov, “On a boundary control problem for a pseudo-parabolic equation”, CAM, 15:2 (2023), 289
F. N. Dekhkonov, E. I. Kuchkorov, “On the Time-Optimal Control Problem Associated with the Heating Process of a Thin Rod”, Lobachevskii J Math, 44:3 (2023), 1134
N. O. Borschev, “PARAMETRIChESKAYa IDENTIFIKATsIYa KOEFFITsIENTA TEPLOPROVODNOSTI PRI VYSOKOINTENSIVNOM TEPLOM NAGREVE S UChETOM TERMIChESKOGO RAZLOZhENIYa”, Vestnik, 11:6 (2023), 390
F. N. Dekhkonov, “On a Time-Optimal Control of Thermal Processes in a Boundary Value Problem”, Lobachevskii J Math, 43:1 (2022), 192
K. V. Perevozhikova, N. A. Manakova, “Chislennoe modelirovanie startovogo upravleniya i finalnogo nablyudeniya v modeli filtratsii zhidkosti”, J. Comp. Eng. Math., 8:1 (2021), 29–45
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