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Global controllability of nonviscous and viscous Burgers-type equations. (English) Zbl 1282.93050

Summary: We deal with both nonviscous and viscous Burgers-type equations on a bounded interval. We study the global exact controllability of these equations when we have three controls: one control is the right member of the equation and is constant with respect to the space variable; the two others are the boundary values. For a first time, we are interested in nonviscous Burgers-type equations and we prove their global exact controllability for every time \(T>0\) with such controls thanks to the return method. Then we prove the global exact controllability of the viscous Burgers equation for every time \(T>0\).

MSC:

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