In this article we study inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of order $\alpha\in(0,1)$ in time, and a second-order elliptic operator with time-dependent coefficients. We establish a well-posedness and a conditional stability result for the inverse problems using a novel perturbation argument and refined regularity estimates of the associated direct problem. Further, we present an algorithm for efficiently and accurately reconstructing the source component, and provide several two-dimensional numerical results showing the feasibility of the recovery.
翻译:在本文中,我们研究了从横向边界观测中从一个分流模型中回收一个时空依赖源组成部分的逆向问题,数学模型涉及一个Djrbashian-Caputo分数衍生物,即及时的美元(0.1美元),以及一个具有时间依赖系数的二级椭圆经营商。我们利用新颖的扰动论证和对相关直接问题的更精确的规律估计,为反向问题确定了一个稳妥和有条件的稳定结果。此外,我们提出了高效和准确地重建源组成部分的算法,并提供了显示回收可行性的若干二维数字结果。