Identification of the pollution source from one-dimensional parabolic equation models
Identification of the pollution source from one-dimensional parabolic equation models
复制标题
DOI：
10.1016/j.amc.2008.03.014
复制
发表时间：
2012-12
期刊：
影响因子：
--
通讯作者：
Zewen Wang;Jijun Liu
中科院分区：
文献类型：
--
作者：
Zewen Wang;Jijun Liu
考虑流域污染源检测的源反问题。点源污染的扩散过程由一维线性抛物型方程描述，其未知源为λ（t）δ（x-s），其中s为点源的位置，λ（t）为点源的振幅。应用源位置的先验信息和解析延拓理论，证明了两种边界状态的两个内部测量的唯一性：一种是具有零Neumann边界数据的有限流域模型，另一种是无限流域模型.最后，给出了一个可实现的反演算法和一些数值例子，表明了我们的反演方案的有效性。
Consider an inverse source problem modeling the pollution source detection in a watershed. The diffusion process due to the point source pollution is governed by a one-dimensional linear parabolic equation with unknown source of the form λ(t)δ(x-s), where s is the location and λ(t) the amplitude of point source. Applying a priori information about the source location and the analytic extension theory, we prove the uniqueness from two interior measurements for the two kinds of boundary state: one is a finite watershed model with zero-Neumann boundary data and the other is an infinite watershed model. Finally, an implementable inversion algorithm together with some numerical examples are presented, which shows the validity of our inversion scheme.