论文标题
从稀疏边界数据中的分数扩散方程中分数顺序和源项的唯一确定
Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data
论文作者
论文摘要
在本文中，对于二维的分数扩散方程，我们研究了一个同时恢复分数顺序的反问题和稀疏边界测量的源项。通过与我们扩散方程相对应的伴随系统，我们在未知数和测量之间构建了有用的定量关系。从拉普拉斯变换和复杂分析中的知识中，唯一定理得到了证明。
In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system corresponding to our diffusion equation, we construct useful quantitative relation between unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.
