On boundary exact controllability of one-dimensional wave equations with weak and strong interior degeneration

被引：8

作者：

Kogut, Peter I. ^{[1
]}

Kupenko, Olga P. ^{[2
,3
]}

Leugering, Guenter ^{[4
]}

机构：

[1] Oles Honchar Dnipro Natl Univ, Dept Differential Equat, Dnipro, Ukraine

[2] Natl Tech Univ Dnipro Polytech, Dnipro Polytech, Dept Syst Anal & Control, Dnipro, Ukraine

[3] Ihor Sikorsky Natl Tech Univ Ukraine, Kiev Polytech Inst, Inst Appl & Syst Anal, Kiev, Ukraine

[4] Univ Erlangen Nurnberg, Dept Mathe Lehrstuhl 2, Cauerstr 11, D-91058 Erlangen, Germany

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 02期

关键词：

boundary control; degenerate wave equation; exact controllability; existence result; weighted Sobolev spaces; OPERATORS;

D O I：

10.1002/mma.7811

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well-posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions. Passing to a relaxed version of the original problem, we discuss existence and uniqueness of solutions, and using the HUM method we derive conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof.

引用

页码：770 / 792

页数：23

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