Geodesic
Optimality conditions in the problem of thermal control with integral-differential equation
The Bulletin of Irkutsk State University. Series Mathematics, Tome 15 (2016), pp. 50-61

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The optimal control problem for thermal process described by Fredholm integral-differential equation is considered. The definition of the weak generalized solution of the boundary problem is given. The algorithm of its construction is presented. It was found that the optimal control should be found as the solution of nonlinear integral equations with additional conditions in the form of differential inequalities with respect to the source functions.
Keywords: a boundary value problem, weak generalized solution, functional, the maximum principle, the optimal control. 
@article{IIGUM_2016_15_a4,
     author = {A. Kerimbekov and R. J. Nametkulova and A. K. Kadirimbetova},
     title = {Optimality conditions in the problem of thermal control with integral-differential equation},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {50--61},
     publisher = {mathdoc},
     volume = {15},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2016_15_a4/}
}
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A. Kerimbekov; R. J. Nametkulova; A. K. Kadirimbetova. Optimality conditions in the problem of thermal control with integral-differential equation. The Bulletin of Irkutsk State University. Series Mathematics, Tome 15 (2016), pp. 50-61. http://geodesic.mathdoc.fr/item/IIGUM_2016_15_a4/