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Remarks on global controllability for the Burgers equation with two control forces. (English) Zbl 1248.93024

Summary: We deal with the viscous Burgers equation. We study the exact controllability properties of this equation with general initial condition when the boundary control is acting at both endpoints of the interval. In a first result, we prove that the global exact null controllability does not hold for small time. In a second one, we prove that the exact controllability result does not hold even for large time.

MSC:

93B05 Controllability
35Q53 KdV equations (Korteweg-de Vries equations)
93C20 Control/observation systems governed by partial differential equations
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