On the null-controllability of the heat exchange process. (English) Zbl 1253.93010

Alimov, Sh.

Eurasian Math. J. 2, No. 3, 5-19 (2011).

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

Keywords:

parabolic type operators; heat conduction equation; control of distributed systems