Geodesic
Generalized solutions of a boundary value problem for thermal conductivity equation on a graph
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 39-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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Generalized solutions of a boundary value problem for thermal conductivity equation on an arbitrary graph are considered. Analogues of corresponding Sobolev spaces which are dense sets in the space of square-integrable functions are constructed. The theorem of unique solvability of a boundary-value problem is proved. The algorithm of determining boundary control in the problem of translating a differential system from the initial state to the desired final one is presented. Bibliogr. 4.
Keywords: boundary value problem on a graph, generalized solutions, a theorem on unique solvability, boundary control. 
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A. S. Volkova. Generalized solutions of a boundary value problem for thermal conductivity equation on a graph. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 39-47. http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a4/

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[3] Volkova A. S., “Generalized solution for elliptic equations in problems of boundary control on a geometric graph”, Processes control and stability, Works of the 43rd Intern. conference of graduate students and students, eds. A. S. Eremin, N. V. Smirnov, Izdat. Dom S.-Peterb. gos. un-ta, S.-Peterburg, 2012, 14–20

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