Conditional stability in determining a zeroth-order coefficient in a half-order fractional diffusion equation by a Carleman estimate
Conditional stability in determining a zeroth-order coefficient in a half-order fractional diffusion equation by a Carleman estimate
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DOI：
10.1088/0266-5611/28/10/105010
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发表时间：
2012-09
期刊：
影响因子：
2.1
通讯作者：
Masahiro Yamamoto;Ying Zhang
中科院分区：
文献类型：
--
作者：
Masahiro Yamamoto;Ying Zhang
研究了一维半阶分数阶时间扩散方程零阶系数的反问题。在对解和系数的正则性作了一定的假设下，我们利用一些额外的数据证明了一个条件稳定估计。关键是Carleman估计，但由于我们没有分数阶扩散方程的Carleman估计，我们进一步取半阶的t-导数以获得主项为的方程。非齐次项与两个系数之差的导数耦合，因此需要一个额外的Carleman估计，这与通常的偏微分方程系数反问题不同。
An inverse problem of determining a zeroth-order coefficient in a one-dimensional fractional diffusion equation of half-order in time is investigated. Under some assumptions on the regularity of the solutions and coefficients, we prove a conditional stability estimate by some additional data. The key is a Carleman estimate, but since we have no Carleman estimates for the fractional diffusion equation, we further take the t-derivative of half-order to obtain the equation where the principal term is . The nonhomogeneous term is coupled with derivatives of the difference between two coefficients, and so we need an additional Carleman estimate, which is different from usual coefficient inverse problems for partial differential equations.