Observability estimates for the wave equation with rough coefficients

被引：6

作者：

Dehmana, Belhassen ^{[1
]}

Ervedoza, Sylvain ^{[2
]}

机构：

[1] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, El Manar 2092, Tunisia

[2] Univ Toulouse, CNRS, UPS IMT, Inst Math Toulouse,UMR 5219, F-31062 Toulouse 9, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2017年 / 355卷 / 05期

关键词：

EXACT CONTROLLABILITY; BOUNDARY;

D O I：

10.1016/j.crma.2017.03.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The goal of this note is to prove observability estimates for the wave equation with a density which is only continuous in the domain, and satisfies some multiplier-type condition only in the sense of distributions. Our main argument is that one can construct suitable approximations of such density by a sequence of smooth densities whose corresponding wave equations are uniformly observable. The end of the argument then consists in a rather standard passage to the limit. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS.

引用

页码：499 / 514

页数：16

共 19 条

[1] SHARP SUFFICIENT CONDITIONS FOR THE OBSERVATION, CONTROL, AND STABILIZATION OF WAVES FROM THE BOUNDARY
BARDOS, C
LEBEAU, G
RAUCH, J
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1992, 30 (05) : 1024 - 1065
[2] Bardos C., 1989, REND SEM MAT U POL T, V46, P11
[3] Burq N, 1997, ASYMPTOTIC ANAL, V14, P157
[4] A necessary and sufficient condition for the exact controllability of the wave equation
Burq, N
Gerard, P
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (07): : 749 - 752
[5] Concentration and lack of observability of waves in highly heterogeneous media
Castro, C
Zuazua, E
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (01) : 39 - 72
[6] Concentration and lack of observability of waves in highly heterogeneous media (vol 164, pg 39, 2002)
Castro, Carlos
Zuazua, Enrique
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 185 (03) : 365 - 377
[7] Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients
Colombini, Ferruccio
Del Santo, Daniele
Fanelli, Francesco
Metivier, Guy
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (10) : 1791 - 1817
[8] DEPENDENCE OF HIGH-FREQUENCY WAVES WITH RESPECT TO POTENTIALS
Dehman, Belhassen
Ervedoza, Sylvain
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (06) : 3722 - 3750
[9] Fanelli F, 2015, ANAL NONLINEAIRE, V32, P245
[10] Fursikov A.V., 1996, Controllability of Evolution Equations

← 1 2 →