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On the stability of an inverse problem for a coupled hyperbolic-parabolic system

发布时间:2022-12-06 作者: 浏览次数:
Speaker: 刘继军 DateTime: 12月9日(周五) 10:30-11:30
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 刘继军,教授,东南大学

Place: 腾讯会议: 124 763 270
Abstract:Carleman estimates are powerful tools for both forward and inverse problems, especially for showing uniqueness of the inverse problems. We consider an inverse problem of determining two stochastic source functions and the initial status simultaneously in a stochastic thermoelastic system, which is constituted of two stochastic equations of different types. To establish the conditional stability in terms of some suitable norms revealing the stochastic property of the governed system, we first establish two Carleman estimates with regular weight function and two large parameters for stochastic parabolic equation and stochastic hyperbolic equation, respectively. Due to the lack of information about the time derivative of wave field at the final time, the stability index with respect to the wave field at final time is found to be halved, which reveals the special characteristic of our inverse problem for the coupling system.