The unique continuation property for second order evolution PDEs

被引：2

作者：

Choulli, Mourad ^{[1
]}

机构：

[1] Univ Lorraine, Nancy, France

来源：

PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 2卷 / 05期

关键词：

Wave equation; Parabolic equation; Schr & ouml; dinger equation; Elliptic equation; Carleman inequality; Pseudo-convexity condition; Non characteristic hypersurface; Property of unique continuation; Observability inequality; OBSERVABILITY INEQUALITIES; CARLEMAN INEQUALITIES; EXACT CONTROLLABILITY; WAVE-EQUATIONS; SYSTEMS; THEOREM;

D O I：

10.1007/s42985-021-00123-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Sch & ouml;dinger 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.

引用

页数：46

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