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On the null-controllability of the heat exchange process. (English) Zbl 1253.93010
Summary: A mathematical model of the heat exchange process, where the temperature inside some domain is controlled by \(m\) convectors acting on the boundary, is considered. The control parameter is a vector-function, whose components are equal to the magnitude of the output of hot or cold air produced by each convector. Necessary and sufficient conditions, which initial temperature must satisfy for achieving the zero value by the projection of the temperature into some \(m\)-dimensional subspace, are studied.

MSC:
93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
35K05 Heat equation
35K20 Initial-boundary value problems for second-order parabolic equations
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