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Regular version of the site

Article

Optimal control problems for wave equations

Journal of Mathematical Sciences. 2011. Vol. 69. No. 2. P. 257-269.
The problem on minimizing a quadratic functional on trajectories of the wave equation is considered. We assume that the density of external forces is a control function. A control problem for a partial differential equation is reduced to a control problem for a countable system of ordinary differential equations by use of the Fourier method. The controllability problem for this countable system is considered. Conditions of the noncontrollability for some wave equations were obtained.