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

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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/}
}
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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/