Geodesic
Optimization of thermal processes in a nonlocal problem with a redefinition function under an integral condition
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 120-130.

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In this paper, we examine the weak generalized solvability of an inverse optimization problem for the heat equation with a nonlocal boundary condition and a nonlinear target performance. We formulate necessary optimality conditions and reduce the search for a control function to a functional integral equation.
Keywords: heat equation, nonlinear inverse problem, optimal control, nonlinear control, minimization of a functional 
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T. K. Yuldashev; G. K. Abdurakhmanova. Optimization of thermal processes in a nonlocal problem with a redefinition function under an integral condition. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 120-130. http://geodesic.mathdoc.fr/item/INTO_2023_229_a9/

[1] Iskenderov A. D., Gamidov R. A., “Zadachi optimizatsii s gradientom upravleniya v koeffitsientakh ellipticheskikh uravnenii”, Avtomat. telemekh., 81:9 (2020), 1627–1636 | MR | Zbl

[2] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982 | MR

[3] Egorov A. I., Optimalnoe upravlenie termicheskimi i diffuzionnymi protsessami, Nauka, M., 1978

[4] Lure K. A., Optimalnoe upravlenie v zadachakh matematicheskoi fiziki, Nauka, M., 1975 | MR

[5] Krotov V. F., Gurman V. I., Metody i zadachi optimalnogo upravleniya, Nauka, M., 1973

[6] Kvitko A. N., “Ob odnom metode resheniya lokalnoi kraevoi zadachi dlya nelineinoi upravlyaemoi sistemy”, Avtomat. telemekh., 81:2 (2020), 236–246 | MR | Zbl

[7] Miller B. M., Rubinovich E. Ya., “Razryvnye resheniya v zadachakh optimalnogo upravleniya i ikh predstavlenie s pomoschyu singulyarnykh prostranstvenno-vremennykh preobrazovanii”, Avtomat. telemekh., 74:12 (2013), 56–103 | Zbl

[8] Pulkina L. S., “Smeshannaya zadacha s integralnym usloviem dlya giperbolicheskogo uravneniya”, Mat. zametki., 74:3 (2003), 435–445 | DOI | MR | Zbl

[9] Rapoport E. Ya., Optimalnoe upravlenie sistemami s raspredelennym parametrom, Vysshaya shkola, M., 2009

[10] Srochko V. A., Iteratsionnye metody resheniya zadach optimalnogo upravleniya, Fizmatlit, M., 2000

[11] Yuldashev T. K., “Optimalnoe upravlenie obratnymi teplovymi protsessami v parabolicheskom uravnenii s nelineinymi otkloneniyami po vremeni”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 210 (2022), 117–135 | DOI

[12] Yuldashev T. K., “Opredelenie koeffitsienta i klassicheskaya razreshimost nelokalnoi kraevoi zadachi dlya integro-differentsialnogo uravneniya Benni—Lyuka s vyrozhdennym yadrom”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 156 (2018), 89–102

[13] Yuldashev T. K., “Obratnaya smeshannaya zadacha dlya integro-differentsialnogo uravneniya s mnogomernym operatorom Benni—Lyuka i nelineinymi maksimumami”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 201 (2021), 3–15 | DOI

[14] Yuldashev T. K., Rakhmonov F. D., Ismoilov A. S., “Integro-differentsialnoe uravnenie Bussineska s integralnymi usloviyami i c malym parametrom pri smeshannykh proizvodnykh”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 211 (2022), 114–130 | DOI

[15] Girsanov I. V., Lectures on the Mathematical Theory of Extremum Problems, Springer-Verlag, New York, 1972 | MR | Zbl

[16] Lions J. L., Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, 1971 | MR | Zbl

[17] Kerimbekov A. K., “On solvability of the nonlinear optimal control problem for processes described by the semilinear parabolic equations”, Proc. World Congress Engineering, Vol. I (London, July 6-8, 2011), 2011, 270–275

[18] Yuldashev T. K., “Nonlinear optimal control of thermal processes in a nonlinear inverse problem”, Lobachevskii J. Math., 41:1 (2020), 124–136 | DOI | MR | Zbl