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This paper studies the time optimal control problem for systems of heatequations coupled by a pair of constant matrices. The control constraint is ofthe ball-type, while the target is the origin of the state space. We obtain anupper bound for the number of switching points of the optimal control over eachinterval with a fixed length. Also, we prove that at each switching point, theoptimal control jump from one direction to the reverse direction.

Switching properties of time optimal controls for systems of heat equations coupled by constant matrices