Geodesic
Optimal control of inverse thermal processes in a parabolic equation with nonlinear deviations in time
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 117-135

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In this paper, we examine the weakly generalized solvability of a nonlinear inverse problem in the nonlinear optimal control of thermal processes for one type of parabolic differential equation with nonlinear deviations. We formulate necessary optimality conditions for nonlinear control and obtain formulas for approximate calculating the state functions of the controlled process, the restoration function, and the optimal control function.
Keywords: nonlinear inverse problem, nonlinear deviation, necessary conditions for optimality of control, nonlinearity of control, minimization of the functional. 
@article{INTO_2022_210_a11,
     author = {T. K. Yuldashev},
     title = {Optimal control of inverse thermal processes in a parabolic equation with nonlinear deviations in time},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {117--135},
     publisher = {mathdoc},
     volume = {210},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_210_a11/}
}
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T. K. Yuldashev. Optimal control of inverse thermal processes in a parabolic equation with nonlinear deviations in time. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 117-135. http://geodesic.mathdoc.fr/item/INTO_2022_210_a11/