一个二维对流扩散方程源项反问题的条件唯一性

Conditional Uniqueness for an Inverse Source Problem in the Two Dimensional Convection-Diffusion Equations

摘要: 本文应用变分伴随方法研究二维对流扩散方程中确定线性连续源项的一个反问题，并基于正问题的伴随问题，建立了一个联系已知数据与未知边界流量的变分恒等式，进而利用对伴随问题的近似控制，在反问题的解满足局部保序性的条件下，证明反问题解的唯一性。

Abstract: This article deals with an inverse problem of determining a continuous linear source term in the two dimensional convection-diffusion equation by using the variational adjoint method. A variational identity connecting the known data with the unknown is established based on an adjoint problem, and the conditional uniqueness to the inverse source problem is proved by the approximate controllability to the adjoint problem under the condition that the inverse solution can keep orders locally.