Control with point observation for a parabolic problem with convection. (English. Russian original) Zbl 1436.35221
Trans. Mosc. Math. Soc. 2019, 221-234 (2019); translation from Tr. Mosk. Mat. O.-va 80, No. 2, 259-274 (2019).
Summary: We consider a control problem related to the mathematical model of temperature control in industrial hothouses. It is based on a one-dimensional non-selfadjoint parabolic equation with variable coefficients. Defining an optimal control as a minimizing function for a quadratic functional, we study its qualitative properties and the structure of the set of admissible temperature functions. We prove controllability for a certain family of control functions.
MSC:
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35Q93 | PDEs in connection with control and optimization |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 93C20 | Control/observation systems governed by partial differential equations |
Keywords:
parabolic equation; extremum problem; quadratic functional; minimizing function; controllability; exact controllabilityReferences:
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