Abstract
The initial-boundary problem for the heat conduction equation inside a bounded domain is considered. It is supposed that on the boundary of this domain the heat exchange according to Newton’s law takes place. The control parameter is equal to the magnitude of output of hot or cold air and is defined on a given part of the boundary. An estimate of the minimal time for achieving the given average temperature is found.
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Albeverio, S., Alimov, S. On a Time-Optimal Control Problem Associated with the Heat Exchange Process. Appl Math Optim 57, 58–68 (2008). https://doi.org/10.1007/s00245-007-9008-7
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DOI: https://doi.org/10.1007/s00245-007-9008-7