Abstract
The Oskolkov model on a geometrical graph describes the process of oil transportation by a system of pipes. Of concern is the stability of solutions and the optimal control of solutions for the operator-differential equation, unsolved with respect to time derivative, with Showalter–Sidorov condition. In this case one of the operators in the equation is multiplied by a scalar function. The existence and uniqueness of the solution of the Showalter–Sidorov problem for the nonautonomous equation are proved. The stability of solutions and the existence of a unique optimal control of solutions of this problem are proved using these results. All obtained results are applied to the research of the linearized Oskolkov model, considered on a graph.
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Sagadeeva, M.A., Sviridyuk, G.A. (2015). The Nonautonomous Linear Oskolkov Model on a Geometrical Graph: The Stability of Solutions and the Optimal Control Problem. In: Banasiak, J., Bobrowski, A., Lachowicz, M. (eds) Semigroups of Operators -Theory and Applications. Springer Proceedings in Mathematics & Statistics, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-12145-1_16
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