Unique continuation and approximate controllability for a degenerate parabolic equation

被引：36

作者：

Cannarsa, Piermarco ^{[1
]}

Tort, Jacques ^{[2
]}

Yamamoto, Masahiro ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Univ Toulouse 3, Inst Math Toulouse, CNRS, UMR 5219, F-31062 Toulouse 4, France

[3] Univ Tokyo, Dept Math Sci, Meguro Ku, Tokyo 1538914, Japan

来源：

APPLICABLE ANALYSIS | 2012年 / 91卷 / 08期

关键词：

degenerate parabolic equations; unique continuation; approximate controllability; local Carleman estimate; NULL CONTROLLABILITY; OPERATORS;

D O I：

10.1080/00036811.2011.639766

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article studies unique continuation for weakly degenerate parabolic equations in one-space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that vanish on the degeneracy set, together with their conormal derivative, are identically equal to zero. An approximate controllability result for weakly degenerate parabolic equations under Dirichlet boundary condition is deduced.

引用

页码：1409 / 1425

页数：17

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