Null-controllability properties of the wave equation withasecond order memory term

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Biccari, Umberto^1,2  Micu, Sorin^3,4 

[1] Univ Deusto, DeustoTech, Bilbao 48007, Basque Country, Spain

[2] Univ Deusto, Fac Ingn, Ave Univ 24, Bilbao 48007, Basque Country, Spain

[3] Univ Craiova, Dept Math, Craiova 200585, Romania

[4] Inst Math Stat & Appl Math, Bucharest 70700, Romania

关键词: Wave equation;    Memory;    Null controllability;    Moving control;    Moment method;   

DOI  :  10.1016/j.jde.2019.02.009

来源: Elsevier

【 摘 要 】

We study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus T = R/2 pi Z. We assume that the control is acting on an open subset omega(t) subset of T, which is moving with a constant velocity c epsilon R \ {-1, 0, 1}. The main result of the paper shows that the equation is null controllable in a sufficiently large time Tand for initial data belonging to suitable Sobolev spaces. Its proof follows from a careful analysis of the spectrum associated with our problem and from the application of the classical moment method. (c) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free