ASYMPTOTIC STABILITY OF INTERMITTENTLY DAMPED SEMI-LINEAR HYPERBOLIC-TYPE EQUATIONS

被引：0

作者：

Luo, Jun-Ren ^{[1
]}

Xiao, Ti-Jun ^{[2
]}

机构：

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2023年 / 22卷 / 01期

关键词：

Intermittent (on-off) damping; asymptotic stability; evolution equation; Hilbert space; WAVE-EQUATION; DECAY; BEHAVIOR; SYSTEM;

D O I：

10.3934/cpaa.2022126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Of concern is asymptotic stability for second order semilinear evolution equations in a Hilbert space with intermittent damping. We obtain asymptotic stability results, without the assumption that the damping coefficient a(t) is always positive, which means that the unique damping term could vanish sometimes. Moreover, we do not need the condition that the main linear operator A is coercive, that is, A could have a non-trivial kernel.

引用

页码：82 / 99

页数：18

共 50 条

[41] SMITH-TYPE STABILITY THEOREMS FOR THE DAMPED LINEAR OSCILLATOR
Hatvani, L.
DYNAMIC SYSTEMS AND APPLICATIONS, 2018, 27 (02): : 299 - 318
[42] Fundamental solution and asymptotic stability of linear delay differential equations
Györi, I
Hartung, F
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2006, 13 (02): : 261 - 287
[43] Asymptotic stability analysis of the linear θ-method for linear parabolic differential equations with delay
Tian, Hongjiong
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2009, 15 (05) : 473 - 487
[44] Scattering for Radial, Semi-Linear, Super-Critical Wave Equations with Bounded Critical Norm
Benjamin Dodson
Andrew Lawrie
Archive for Rational Mechanics and Analysis, 2015, 218 : 1459 - 1529
[45] Critical curve for a weakly coupled system of semi-linear σ-evolution equations with different damping types
Duong, Dinh Van
Dao, Tuan Anh
Reissig, Michael
JOURNAL OF EVOLUTION EQUATIONS, 2025, 25 (02)
[46] POSITIVE SUPER-SOLUTIONS TO SEMI-LINEAR SECOND-ORDER NON-DIVERGENCE TYPE ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS
Kondratiev, Vladimir
Liskevich, Vitali
Sobol, Zeev
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (02) : 697 - 713
[47] Well-posedness and stability results for some nonautonomous abstract linear hyperbolic equations with memory
Al-Khulaifi, Waled
Diagana, Toka
Guesmia, Aissa
SEMIGROUP FORUM, 2022, 105 (02) : 351 - 373
[48] Asymptotic stability of some nonlinear Boltzmann-type equations
Lasota, A
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 268 (01) : 291 - 309
[49] On explicit conditions for the asymptotic stability of linear higher order difference equations
Liz, E
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (02) : 492 - 498
[50] ON ASYMPTOTIC STABILITY OF SOLUTIONS OF SECOND ORDER LINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS
Barinova, Tatiyana
Kostin, Alexander
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2014, 63 : 79 - 104

← 1 2 3 4 5 →