Stabilization of coupled thermoelastic Kirchhoff plate and wave equations
We consider a coupled system consisting of a Kirchhoff thermoelastic plate and an undamped wave equation. It is known that the Kirchhoff thermoelastic plate is exponentially stable. The coupling is weak. First, we show that the coupled system is not exponentially stable. Afterwards, we prove that...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/121/abstr.html |
| Summary: | We consider a coupled system consisting of a Kirchhoff thermoelastic plate and an
undamped wave equation. It is known that the Kirchhoff thermoelastic plate is
exponentially stable. The coupling is weak. First, we show that the coupled system is
not exponentially stable. Afterwards, we prove that the coupled system is polynomially
stable, and provide an explicit polynomial decay rate of the associated semigroup.
Our proof relies on a combination of the frequency domain method and the multipliers
technique. |
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| ISSN: | 1072-6691 |