Abstract
I.M. Gali et al have considered a distributed control problem for hyperbolic operator with an infinite number of variables [6]. Also they established the solvability of the mixed problem for nonlinear infinite order hyperbolic equations [7]. The authors in [9] have obtained the set of inequalities defining an optimal control of a system governed by infinite tensor product of elliptic operators Ak.
In the present paper, a distributed control problem for the hyperbolic operator 
is considered.
The necessary and sufficient condition for the control to be optimal is obtained, and the set of inequalities that characterize this condition is also obtained.
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References
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Gali, I.M., El-Saify, H.A., El-Zahabi, S.A. (1985). Optimal control of a system governed by hyperbolic operator. In: Sleeman, B.D., Jarvis, R.J. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 1151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074724
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DOI: https://doi.org/10.1007/BFb0074724
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