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Minimal time of null controllability of two parabolic equations. (English) Zbl 1442.93010

Summary: We consider a one-dimensional \(2 \times 2\) parabolic equations, simultaneously controllable by a localized function in their source term. We also consider a simultaneous boundary control. In each case, we prove the existence of minimal time \(T_0(q)\) of null controllability, that is to say, the corresponding problem is null controllable at any time \(T > T_0(q)\) and not null controllable for \(T < T_0(q)\). We also prove that one can expect any minimal time associated to the boundary control problem.

MSC:

93B05 Controllability
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
35K20 Initial-boundary value problems for second-order parabolic equations
93C20 Control/observation systems governed by partial differential equations
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