论文标题
同时确定来自单个测量的系数，内部来源和扩散方程的障碍物
Simultaneous determination of coefficients, internal sources and an obstacle of a diffusion equation from a single measurement
论文作者
论文摘要
本文专门针对三个反问题的同时解决，这是部分微分方程的反问题的最重要的表述中，从单个边界测量中指出了某些类别的扩散方程。也就是说，我们考虑了几类系数，某些内部源（源项和初始条件）以及从单个边界测量中出现的扩散方程中出现的障碍。我们的问题可以被提出为同时确定有关扩散过程（速度场，介质的密度），障碍物和扩散来源的信息。我们认为在用对流扩散方程描述的经典扩散过程以及由时间分数扩散方程描述的异常扩散现象所描述的环境中。
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single boundary measurement. Namely, we consider the simultaneous unique determination of several class of coefficients, some internal sources (a source term and an initial condition) and an obstacle appearing in a diffusion equation from a single boundary measurement. Our problem can be formulated as the simultaneous determination of information about a diffusion process (velocity field, density of the medium), an obstacle and of the source of diffusion. We consider this problems in the context of a classical diffusion process described by a convection-diffusion equation as well as an anomalous diffusion phenomena described by a time fractional diffusion equation.
