Inverse problems for the Boussinesq system
Inverse problems for the Boussinesq system
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DOI：
10.1088/0266-5611/25/8/085007
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发表时间：
2009-08
期刊：
影响因子：
2.1
通讯作者：
Jishan Fan;Yu Jiang;G. Nakamura
中科院分区：
文献类型：
--
作者：
Jishan Fan;Yu Jiang;G. Nakamura
我们得到了二维Boussinesq系统反问题的两个结果。一是利用速度在任意时间区间内的子域观测数据和速度和温度在整个空间域的固定正时间范围内的数据，证明了识别系统中时间无关外力的逆源问题的Lipschitz稳定性。另一方面，我们证明了在子域上用单次观测识别两个初始条件的反问题的条件稳定性估计。
We obtain two results on inverse problems for a 2D Boussinesq system. One is that we prove the Lipschitz stability for the inverse source problem of identifying a time-independent external force in the system with observation data in an arbitrary sub-domain over a time interval of the velocity and the data of velocity and temperature at a fixed positive time t0 > 0 over the whole spatial domain. The other one is that we prove a conditional stability estimate for an inverse problem of identifying the two initial conditions with a single observation on a sub-domain.