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Polynomial decay and control of a 1D hyperbolic-parabolic coupled system. (English) Zbl 1064.93008

The paper considers a coupled (via interaction through the joint boundary) 1D system of the heat and wave equation. In the first part of the paper the spectral analysis of the system is given and on its basis sharp polynomial decay rates for the whole energy are obtained. In the second part the null-controllability of the system when the control acts on the boundary of the domain where the heat equation holds is analyzed.

MSC:

93B05 Controllability
35B37 PDE in connection with control problems (MSC2000)
93B07 Observability
93C20 Control/observation systems governed by partial differential equations
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