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Frequency domain approach to decay rates for a coupled hyperbolic-parabolic system

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This work is partially supported by the NSF of China under grants 11931011, 11821001 and 11831011, and by the Science Development Project of Sichuan University under grant 2020SCUNL201

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  • We consider the asymptotic behavior of a linear model arising in fluid-structure interactions. The system is formed by a heat equation and a wave equation in two distinct domains, which are coupled by atransmission condition along the interface of the domains. By means of the frequency domain approach, we establish some decay rates for the whole system. Our results also showthat the decay of the fluid-structure interaction depends not only on the transmission of the damping from the heat equation to the wave equation, but also on the location of the damping for the wave equation.

    Mathematics Subject Classification: Primary: 35B35, 37L15; Secondary: 74F10, 93D20.


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