Stabilization of a coupled hyperbolic equations with a heat equation of second sound. (English) Zbl 1371.35307
Summary: In this article, we study the energy decay rate for a coupled hyperbolic-parabolic system where the heat conduction is given via Catteneo’s law. The system consists of two wave equations and two heat equations coupled in a certain pattern. We proved an exponential decay result which depends on a new stability number \(\chi_0\). We proved the polynomial decay result with an estimation of the decay rates. Our result is established using the frequency-domain method.
MSC:
| 35Q93 | PDEs in connection with control and optimization |
| 93D15 | Stabilization of systems by feedback |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74F05 | Thermal effects in solid mechanics |
| 35B35 | Stability in context of PDEs |
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