Geodesic
Optimum control of parabolic system with the distributed parameters on~the graph
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2014), pp. 154-163

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The initial and regional task for the parabolic equation with distributed is considered parameters on limited graph $\Gamma$ and it the corresponding problem of optimum control. Work continues researches of the author in the direction of existence and uniqueness optimum control in a case, when a condition of differential system an essence display of a piece of $[0,T]$ ($T\infty$) in special space. Thus in quality of space of managements the space of functions integrated with a square is used $L_2(\Gamma_T)$, $\Gamma_T=\Gamma\times(0,T)$. Bibliogr. 13.
Keywords: initial and regional task with the distributed parameters on the graph, the generalized decision, optimum control. 
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     author = {V. V. Provotorov},
     title = {Optimum control of parabolic system with the distributed parameters on~the graph},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {154--163},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2014_3_a14/}
}
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V. V. Provotorov. Optimum control of parabolic system with the distributed parameters on~the graph. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2014), pp. 154-163. http://geodesic.mathdoc.fr/item/VSPUI_2014_3_a14/