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Controllability properties for the one-dimensional heat equation under multiplicative or nonnegative additive controls with local mobile support. (English) Zbl 1262.35119
Summary: We discuss several new results on nonnegative approximate controllability for the one-dimensional heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.

35K20 Initial-boundary value problems for second-order parabolic equations
35K05 Heat equation
93B05 Controllability
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