论文标题
二阶进化PDE的独特延续的属性
The property of unique continuation for second order evolution PDEs
论文作者
论文摘要
我们提出了一种简单且独立的方法，以建立圆柱域中二阶经典演化方程的独特延续性。我们即将与时间独立的主要部分讨论Wave，抛物线和Schödinger运营商的此属性。我们的方法是建立在两参数Carleman不平等的基础上，结合了相对于空间变量的伪凸高超出表面的独特延续。我们在这项工作中证明的最大结果或多或少是古典的。其中一些并不像原始形式那样完全说明。
We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and Schödinger operators with time-independent principal part. Our method is builds on two-parameter Carleman inequalities combined with unique continuation across a pseudo-convex hypersurface with respect to the space variable. The most results we demonstrate in this work are more or less classical. Some of them are not stated exactly as in their original form.
