利用观测数据确定传导方程系数的稳定性

Determination of stability of conductivity coefficient by boundary measurements

本文目的研究利用边界上有限多个观测数据确定传导方程div(a▽u)=0系数a(x)的逆问题.众所周知,在Hadamard意义下这是一个不适定问题.通过对Dirichlet-Neumann映射Λa性质的研究,在a∈Hs+2假设条件下,得到了条件稳定性估计.

In this article,we investigate the inverse problem of determining the coefficient a(x) of the conductivity equation div(a▽u) =0 from finite measurements on the boundary.It is well known that this is an ill-posed problem in the sense of Hadamard.The conditional stability estimation is proved under the assumption of a ∈ Hs+2 by using properties of the Dirichlet-Neumann map Λa.