论文标题
波浪运营商的定量独特延续，跨接口和应用程序近似控制
Quantitative unique continuation for wave operators with a jump discontinuity across an interface and applications to approximate control
论文作者
论文摘要
在本文中，我们证明了$ \ partial $ 2 t的波浪运算符的定量唯一连续性结果 - div（c（x）$ \ nabla $$ \ bullet \ bullet $），其中标量系数C在有限域或紧凑型riemannian歧管上的编辑界面上不连续。我们对界面的几何形状或系数c的跳跃符号没有任何假设。关键成分是具有不连续系数的波浪运算符的本地卡尔曼估计。然后，我们将此估计与laurent-l {é} Autaud [ll19]的最新技术相结合，以传播本地独特的延续估计并获得全球稳定性不平等。结果，我们推断出在该几何形状中传播的波的近似可控性的成本。
In this article we prove quantitative unique continuation results for wave operators of the form $\partial$ 2 t -- div(c(x)$\nabla$$\bullet$) where the scalar coefficient c is discontinuous across an interface of codimension one in a bounded domain or on a compact Riemannian manifold. We do not make any assumptions on the geometry of the interface or on the sign of the jumps of the coefficient c. The key ingredient is a local Carleman estimate for a wave operator with discontinuous coefficients. We then combine this estimate with the recent techniques of Laurent-L{é}autaud [LL19] to propagate local unique continuation estimates and obtain a global stability inequality. As a consequence, we deduce the cost of the approximate controllability for waves propagating in this geometry.
