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Null controllability of the semilinear heat equation. (English) Zbl 0897.93011

The author considers a control system governed by semilinear parabolic equations. The control acts either on a small subdomain or on a part of the boundary. He proves the null controllability property provided that the nonlinearity \(f(\cdot)\) is locally Lipschitz continuous, \(f(0)=0\) and \[ \lim_{| s| \rightarrow\infty} {{f(s)}\over {s\log | s| }}=0. \] The approach is based on Schauder’s fixed-point theorem.
Reviewer: O.Cârjá (Iaşi)

MSC:

93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
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References:

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