论文标题
具有非零边界条件的一维时折射方程的逆系数问题的唯一性
Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions
论文作者
论文摘要
我们考虑了一维扩散方程的初始边界值问题，该方程与（0,1）$的订单$α\的时间折叠导数，该阶数受到非零neumann边界条件的约束。我们证明了一个逆系数问题的唯一性，即确定空间差异衍生物的空间变化势和时间折叠派生的顺序在空间间隔的一个端点上。施加的Neumann条件必须在订单$α$的正确Sobolev空间内。我们的证明是基于用非零边界数据的初始边界值问题的表示解决方案的表示公式。此外，我们应用了这样的公式，并证明了Cauchy Data在一个端点的另一个端点确定边界值的唯一性。
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $α\in (0,1)$ 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.
