Ervedoza和Zuazua关于heat equation在小时间内可观测性的猜想在Coron和Guerrero关于对流-扩散方程一致能控性的猜想中的应用
An application of a conjecture due to Ervedoza and Zuazua concerning the observability of the heat equation in small time to a conjecture due to Coron and Guerrero concerning the uniform controllability of a convection-diffusion equation
摘要：
这篇短文的目的是探讨一个关于1-D热方程在短时间内的锐边界可观测性估计的猜想和一个关于1-D对流-扩散方程在边界上具有常系数控制的零能控性代价的猜想之间的一个新的联系，在[Pierre Lissy，研究了一维热传导方程的快速控制代价与一维输运-扩散方程的一致能控性之间的联系。R.数学学院Sci.巴黎，第352卷，2012年]。我们特别证明了当输运-扩散方程中输运部分的速度为非负时，第一个猜想蕴涵第二个猜想。
英文摘要：
The aim of this short paper is to explore a new connection between a conjecture concerning sharp boundary observability estimates for the 1-D heat equation in small time and a conjecture concerning the cost of null-controllability for a 1-D convection-diffusion equation with constant coefficients controlled on the boundary in the vanishing viscosity limit, in the spirit of what is done in [Pierre Lissy, A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation, C. R. Math. Acad. Sci. Paris, Volume 352, 2012]. We notably establish that the first conjecture implies the second one as soon as the speed of the transport part is non-negative in the transport-diffusion equation.
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