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Null controllability for a class of degenerate parabolic equations with the gradient terms. (English) Zbl 1416.93030

Summary: This paper concerns a class of control systems governed by degenerate parabolic equations with the gradient terms, which are independent of the diffusion terms. The Carleman estimates and the observability inequalities for the equations are established when the degeneracy is relatively weak. Subsequently, it is proved that the control systems are null controllable. Moreover, the result can be generalized to the semilinear equations by using the fixed point theorem.

MSC:

93B05 Controllability
93B07 Observability
93C20 Control/observation systems governed by partial differential equations
35K65 Degenerate parabolic equations
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