Research demonstrates a controllability criterion for a partial differential system, indicating a new solution approach.
A controllability criterion for a partial differential system with a small parameter multiplying the second derivative is obtained. The equivalence of this criterion to the Kalman criterion is proved. The control and state functions are constructed explicitly, and the solution of the limit problem is found in closed form. The problem of constructing a control generating a boundary layer phenomenon near two boundaries of a rectangular domain is solved.
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E. V. Raetskaya (2025) studied this question.
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