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Exact controllability for a thermodiffusion system with locally distributed controls. (English) Zbl 1382.35082

Summary: In this work we establish a exact controllability result for a thermodiffusion system, modeled by Cattaneo’s law, posed in a one-dimensional domain. In the present model the control mechanisms are effective in a small subinterval of the domain. To obtain the desired results, we prove an observability inequality for the adjoint system which, together with the multiplier methods and the Hilbert Uniqueness Method (HUM) developed by J. L. Lions, gives the controllability.

MSC:

35G46 Initial-boundary value problems for systems of linear higher-order PDEs
35Q93 PDEs in connection with control and optimization
74F05 Thermal effects in solid mechanics
93B05 Controllability
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