论文标题
可允许几何形状中时间依赖的对流扩散方程的逆问题
Inverse problem for a time-dependent Convection-diffusion equation in admissible geometries
论文作者
论文摘要
我们考虑了可允许的歧管上时间依赖的对流扩散方程的部分数据反问题。我们证明，时间依赖性对流项和时间依赖性密度可以独特地恢复已知的规格不变性。关于欧几里得和里曼尼亚几何学设置的稳态对流扩散操作员以及稳态对流扩散操作员有关的相反问题的作品。但是，在先前的作品中未研究与歧管上与时间有关的对流扩散方程相关的反问题，这是本文的主要目的。实际上，据我们所知，这里研究的问题是与部分数据逆问题有关的第一项工作，用于恢复Riemannian几何形状设置中进化方程的第一和零级时间依赖时间的扰动。
We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known gauge invariance. There have been several works on inverse problems related to the steady state convection-diffusion operator in Euclidean as well as in Riemannian geometry settings; however, inverse problems related to time-dependent convection-diffusion equation on a manifold are not studied in the prior works, which is the main aim of this paper. In fact, to the best of our knowledge, the problem studied here is the first work related to a partial data inverse problem for recovering both first and zeroth-order time-dependent perturbations of evolution equations in the Riemannian geometry setting.
