标题： 扩散方程在R^N中的等分布集上的定量唯一性延续和可观测性 显示英文标题

标题： Quantitative unique continuation and observability on an equidistributed set for the diffusion equation in R^N

摘要： 在本文中，我们得到了整个空间 RN 中扩散方程解的唯一延拓的定量估计以及从等分布集出发的可观测性不等式。这种可观测性表明，解的总能量可以通过在整体空间中等分布的可测子集中的局部能量来控制。我们结果的证明基于一种有趣的约简方法 [18, 22]，以及椭圆方程解的梯度的小值传播 [24]。 显示英文摘要

摘要： In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the whole space RN. This kind of observability indicates that the total energy of solutions can be controlled by the energy localized in a measurable subset, which is equidistributed over the whole space. The proof of our results is based on an interesting reduction method [18, 22], as well as the propagation of smallness for the gradient of solutions to elliptic equations [24].