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
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。
Abstract: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.
文章引用：刘倩. 矩形域上的二维对流扩散方程边界流量反问题[J]. 应用数学进展, 2018, 7(10): 1357-1367. https://doi.org/10.12677/AAM.2018.710158

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