Determination of source terms in a degenerate parabolic equation
Determination of source terms in a degenerate parabolic equation
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DOI：
10.1088/0266-5611/26/10/105003
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发表时间：
2010-10
期刊：
影响因子：
2.1
通讯作者：
P. Cannarsa;J. Tort;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
P. Cannarsa;J. Tort;Masahiro Yamamoto
本文证明了抛物型方程源反问题的Lipschitz稳定性结果。我们使用Imanuvilov和Yamamoto在1998年提出的基于Carleman估计的方法。本文的创新之处在于研究了一类一维退化抛物型方程。在我们的模型中，扩散系数在区域的一个端点处为零。代替经典的Carleman估计获得的Fursikov和Imanuvilov的非退化方程，我们使用和推广最近的Carleman估计退化方程获得的Cannarsa，Martinez和Vancostenoble。最后，我们得到了Lipschitz稳定性结果的反源问题，我们的类退化抛物型方程的情况下，在边界观测和局部分布观测。
In this paper, we prove Lipschitz stability results for inverse source problems relative to parabolic equations. We use the method introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates. What is new here is that we study a class of one-dimensional degenerate parabolic equations. In our model, the diffusion coefficient vanishes at one extreme point of the domain. Instead of the classical Carleman estimates obtained by Fursikov and Imanuvilov for non degenerate equations, we use and extend some recent Carleman estimates for degenerate equations obtained by Cannarsa, Martinez and Vancostenoble. Finally, we obtain Lipschitz stability results in inverse source problems for our class of degenerate parabolic equations both in the case of a boundary observation and in the case of a locally distributed observation.