矩形域上的二维对流扩散方程边界流量反问题  

Inverse Problems of Boundary Flux in the Two-Dimensional Convection-Diffusion Equation in a Rectangular Domain

作　　者：刘倩 

机构地区：[1]山东外贸职业学院泰安校区,山东泰安

出　　处：《应用数学进展》2018年第10期1357-1367,共11页Advances in Applied Mathematics

摘　　要：对于给出的二维对流扩散方程,考虑一个确定边界流量的反问题。应用变分伴随方法,基于联系附加数据和未知边界流量的变分恒等式,证明反问题解的条件唯一性,并建立反问题的Lipschitz稳定性。基于ADI差分方法对正问题进行数值求解,并利用同论正则化方法对边界流量进行数值反演。This article deals with an inverse problem of determining the boundary flux in the two-dimensional convection-diffusion equation in a rectangular domain. Similarly to the method used in my previous paper, a conditional uniqueness and Lipschitz stability for the inverse boundary problem are proved based on a variational identity and controllability to an adjoint problem. Moreover, the ADI scheme is applied to solve the forward problem, and numerical inversions are performed also utilizing the homotopy regulrizarion algorithm.

关 键 词：对流扩散方程 边界流量 反问题 变分伴随方法 条件唯一性 LIPSCHITZ稳定性 数值反演 

分 类 号：O1[理学—数学]