Exponential stability and exact controllability of a system of coupled wave equations by second-order terms (via Laplacian) with only one non-smooth local damping

被引：4

作者：

Akil, Mohammad ^{[1
,3
]}

Hajjej, Zayd ^{[2
]}

机构：

[1] Univ Polytech Hauts France, INSA Hauts France, CERAMATHS Lab Materiaux Ceram & Math, Valenciennes, France

[2] King Saud Univ, Coll Sci, Dept Math, Riyadh, Saudi Arabia

[3] Univ Polytech Hauts France, INSA Hauts France, CERAMATHS Lab Materiaux Ceram & Math, F-59313 Valenciennes, France

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 04期

关键词：

Carleman estimate; controllability; exponential stability; frequency domain approach; geometric condition; HUM method; viscous damping; wave equation; INDIRECT BOUNDARY STABILIZATION; PIEZOELECTRIC BEAMS; OBSERVABILITY; STABILIZABILITY; DECAY;

D O I：

10.1002/mma.9724

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this work is to investigate the exponential stability of a second-order coupled wave equations by Laplacian with one locally internal viscous damping. The strong stability is established by combining a unique continuation result and a Carleman estimate. Besides, the exponential stability is proved under (PMGC) condition on the damping region without any restriction on wave propagation speed (i.e., whether the two wave equations propagate at the same speed or not). The proof of this result relies on the frequency domain method combined with the multiplier techniques.

引用

页码：1883 / 1902

页数：20

共 51 条

[1] OPTIMAL INDIRECT STABILITY OF A WEAKLY DAMPED ELASTIC ABSTRACT SYSTEM OF SECOND ORDER EQUATIONS COUPLED BY VELOCITIES [J].

Abdallah, Farah ;

Ghader, Mouhammad ;

Wehbe, Ali ;

Chitour, Yacine .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2019, 18 (05) :2813-2842

[2] PIEZOELECTRIC BEAMS WITH MAGNETIC EFFECT AND LOCALIZED DAMPING [J].

Afilal, Mounir ;

Soufyane, Abdelaziz ;

Santos, Mauro de Lima .

MATHEMATICAL CONTROL AND RELATED FIELDS, 2021, :250-264

[3]

Akil M., 2021, SeMA J, V78, P287

[4]

Akil M., 2022, POLYNOMIAL ENERGY DE

[5]

Akil M., 2023, ARXIV

[6]

Akil M., 2023, N DIMENSIONAL ELASTI, V80, P425

[7] Stabilization of Coupled Wave Equations with Viscous Damping on Cylindrical and Non-regular Domains: Cases Without the Geometric Control Condition [J].

Akil, Mohammad ;

Badawi, Haidar ;

Nicaise, Serge ;

Regnier, Virginie .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (06)

[8] Stability of piezoelectric beam with magnetic effect under (Coleman or Pipkin)-Gurtin thermal law [J].

Akil, Mohammad .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (06)

[9] Indirect stability of a multidimensional coupled wave equations with one locally boundary fractional damping [J].

Akil, Mohammad ;

Wehbe, Ali .

MATHEMATISCHE NACHRICHTEN, 2022, 295 (12) :2272-2300

[10] Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint [J].

Akil, Mohammad ;

Badawi, Haidar ;

Nicaise, Serge .

COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (06)

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