论文标题
具有广义阻抗子区域的子扩散方程的直接和反面问题
The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion
论文作者
论文摘要
在本文中，我们考虑了具有无法穿透子区域的域中时间分数扩散的直接和反问题。在这里，我们假设在子区域的边界上，解决方案满足了广义的阻抗边界条件。这种边界条件由施加在边界上的二阶空间差分操作员给出。通用阻抗边界条件可用于建模腐蚀和划界。在使用拉普拉斯变换来研究时间依赖的边界值问题的情况下，建立了直接问题的适当性。还要研究从库奇数据确定参数的反阻抗问题，只要已知子区域的边界。证明了从诺伊曼到dirichlet映射恢复边界参数的唯一性。
In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary condition. This boundary condition is given by a second order spacial differential operator imposed on the boundary. A generalized impedance boundary condition can be used to model corrosion and delimitation. The well-posedness for the direct problem is established where the Laplace Transform is used to study the time dependent boundary value problem. The inverse impedance problem of determining the parameters from the Cauchy data is also studied provided the boundary of the subregion is known. The uniqueness of recovering the boundary parameters from the Neumann to Dirichlet mapping is proven.
