Title: Solvability of start control problems for semilinear distributed Sobolev type systems

Authors: V.E. Fedorov, M.V. Plekhanova

Addresses: Department of Mathematical Analysis, Mathematical Faculty, Chelyabinsk State University, Kashirin Brothers Str., 129, Chelyabinsk, 454021, Russia. ' Department of Mathematical Analysis, Mathematical Faculty, Chelyabinsk State University, Kashirin Brothers Str., 129, Chelyabinsk, 454021, Russia

Abstract: In this paper the existence of solutions of start control problem for the system described by first order semilinear equation in Hilbert space with degenerate operator at derivative is researched. For this purpose, sufficient conditions for the existence of a unique solution of the Cauchy problem for the equation are found. The solvability of the start control problem is proved under the assumption of the relative sectoriality of linear operators in the equation, some minimal assumptions for non-linear operator and the condition of the existence of at least one solution for the corresponding Cauchy problem on given interval. Abstract result is illustrated by an example of start control problem for semilinear system of partial integro-differential equations.

Keywords: optimal control; distributed systems; Sobolev type equations; start control; first order semilinear equations.

DOI: 10.1504/IJMMNO.2010.031746

International Journal of Mathematical Modelling and Numerical Optimisation, 2010 Vol.1 No.3, pp.153 - 167

Published online: 22 Feb 2010 *

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