论文标题
非局部扩散方程的Calderón问题与时间相关系数
The Calderón problem for a nonlocal diffusion equation with time-dependent coefficients
论文作者
论文摘要
我们研究了在一个方向界定的域上非局部扩散方程的反问题的全局唯一性。该系数被认为是未知的，并且在整个空间上是各向同性的。我们首先表明部分外部dirichlet to-neumann映射本地确定了外部域中的扩散系数。此外，我们引入了非局部诺伊曼衍生物的新分析，以证明内部确定结果。内部和外部确定产生了与时间相关系数的非局部扩散方程问题的calderón问题所需的全局唯一性定理。这项工作将最新的研究从具有全球系数的非局部椭圆方程式扩展到其抛物线。任何空间尺寸$ n \ geq 1 $都保留的结果。
We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the partial exterior Dirichlet-to-Neumann map locally determines the diffusion coefficient in the exterior domain. In addition, we introduce a novel analysis of nonlocal Neumann derivatives to prove an interior determination result. Interior and exterior determination yield the desired global uniqueness theorem for the Calderón problem of nonlocal diffusion equations with time-dependent coefficients. This work extends recent studies from nonlocal elliptic equations with global coefficients to their parabolic counterparts. The results hold for any spatial dimension $n\geq 1$.
