Geodesic
Variational method for solving a coefficient inverse problem for a parabolic equation with integral conditions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 133-141

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In this paper, we consider an inverse control-type problem of determining the minor coefficient of a parabolic equation with an integral boundary-value condition and an additional integral condition. The well-posedness of the problem is examined. The Fréchet differentiability of the target functional based on the additional integral condition is proved and an expression for its gradient is found. A necessary condition for the optimality of control is established.
Keywords: inverse problem, integral boundary condition, correctness of the problem, necessary optimality condition.
Mots-clés : parabolic equation 
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     author = {R. K. Tagiyev and Sh. I. Maharramli},
     title = {Variational method for solving a coefficient inverse problem for a parabolic equation with integral conditions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {133--141},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a15/}
}
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R. K. Tagiyev; Sh. I. Maharramli. Variational method for solving a coefficient inverse problem for a parabolic equation with integral conditions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 133-141. http://geodesic.mathdoc.fr/item/INTO_2023_224_a15/