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Null controllability of the Burgers system with distributed controls. (English) Zbl 1130.93015

Summary: This paper is devoted to present some positive and negative controllability results for the viscous Burgers equation. More precisely, in the context of null controllability with distributed controls, we present sharp estimates of the minimal time of controllability \(T(r)\) of initial data of \(L^{2}\)-less or equal to \(r\). In particular, we see that (global) null controllability does not hold in general (unless the control is exerted everywhere). The same results apply to similar boundary controllability systems with one boundary control.

MSC:

93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
93C10 Nonlinear systems in control theory
35B37 PDE in connection with control problems (MSC2000)
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