Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions
Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions
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DOI：
10.1080/00036811.2021.1965583
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发表时间：
2020-09
影响因子：
1.1
通讯作者：
W. Rundell;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
W. Rundell;Masahiro Yamamoto
研究了一类带时间分数阶导数的一维扩散方程的初边值问题，该问题具有非零Neumann边界条件。我们证明了反系数问题的唯一性，确定一个空间变化的潜力和时间分数阶导数的Dirichlet数据在一个端点的空间间隔。所施加的诺依曼条件必须在正确的α阶Sobolev空间内。我们的证明是基于非零边界数据的初边值问题的解的表示公式。应用此公式，证明了由一个端点的柯西数据确定另一个端点的边值的唯一性。
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse coefficient problem of determining a spatially varying potential and the order of the time-fractional derivative by Dirichlet data at one end point of the spatial interval. The imposed Neumann conditions are required to be within the correct Sobolev space of order α. Our proof is based on a representation formula of solution to an initial boundary value problem with non-zero boundary data. Moreover, we apply such a formula and prove the uniqueness in the determination of boundary value at another end point by Cauchy data at one end point.