On the existence of an optimal solution of the Mayer problem governed by 2D continuous counterpart of the Fornasini-Marchesini model Authors Dorota Bors Faculty of Mathematics and Computer Science University of Lodz Marek Majewski Faculty of Mathematics and Computer Science University of Lodz Open Access Article

First Online: 23 October 2012 Received: 30 May 2012 Revised: 04 October 2012 Accepted: 10 October 2012 DOI :
10.1007/s11045-012-0207-2

Cite this article as: Bors, D. & Majewski, M. Multidim Syst Sign Process (2013) 24: 657. doi:10.1007/s11045-012-0207-2
Abstract In the paper the optimization problem described by some nonlinear hyperbolic equation being continuous counterpart of the Fornasini-Marchesini model is considered. A theorem on the existence of at least one solution to this hyperbolic PDE is proved and some properties of the set of all solutions are established. The existence of a solution to an optimization problem under appropriate assumptions is the main result of this paper. Some application of the obtained results to the process of gas filtration is also presented.

Keywords Mayer problem Continuous counterpart of the Fornasini-Marchesini model Existence of optimal solutions Download to read the full article text

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