Decay property for nonlinear damped wave equations in one space dimension

被引：0

作者：

Katayama, Soichiro ^{[1
]}

Wakasa, Kyouhei ^{[2
]}

Yordanov, Borislav ^{[3
]}

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, 1-1 Machikaneyama Cho, Toyonaka, Osaka 5600043, Japan

[2] Natl Inst Technol, Kushiro Coll, Dept Creat Engn, 2-32-1 Otanoshike Nishi, Kushiro, Hokkaido 0840916, Japan

[3] Bulgarian Acad Sci, Inst Math & Informat, 8 Akad,Georgi Bonchev Str, Sofia 1113, Bulgaria

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 404卷

关键词：

Nonlinear wave equation; Nonlinear damping; Energy decay; Pointwise decay; ENERGY DECAY;

D O I：

10.1016/j.jde.2024.05.048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the wave equation with a nonlinear dissipative term in one space dimension. When the power of the nonlinearity is greater than two, we get a pointwise decay estimate for solutions, from which we also obtain the energy decay result by using the L1 -estimate of Haraux [1]. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：279 / 296

页数：18

共 50 条

[41] A property of exponential stability in nonlinear wave equations near the fundamental linear mode
Bambusi, D
Nekhoroshev, NN
PHYSICA D-NONLINEAR PHENOMENA, 1998, 122 (1-4) : 73 - 104
[42] Energy decay for wave equations with a potential and a localized damping
Xiaoyan Li
Ryo Ikehata
Nonlinear Differential Equations and Applications NoDEA, 2024, 31
[43] Exponential energy decay of solutions of viscoelastic wave equations
Wang, Yanjin
Wang, Yufeng
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 347 (01) : 18 - 25
[44] ATTRACTORS FOR WAVE EQUATIONS WITH NONLINEAR DAMPING ON TIME-DEPENDENT SPACE
Meng, Fengjuan
Yang, Meihua
Zhong, Chengkui
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2016, 21 (01): : 205 - 225
[45] Energy decay for wave equations with a potential and a localized damping
Li, Xiaoyan
Ikehata, Ryo
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (02):
[46] Global existence and energy decay result for a weak viscoelastic wave equations with a dynamic boundary and nonlinear delay term
Ferhat, Mohamed
Hakem, Ali
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 71 (03) : 779 - 804
[47] Energy decay for the nonlinear wave equation with a half-linear dissipation in RN
Jung, Il Hyo
Kang, Yong Han
ASYMPTOTIC ANALYSIS, 2006, 48 (1-2) : 19 - 32
[48] A sufficient condition for global existence of the solution to nonlinear damped wave equations at arbitrary positive initial energy
Chen, Yuxuan
Li, Yanan
MATHEMATISCHE NACHRICHTEN, 2023, 296 (12) : 5703 - 5709
[49] SHARP POLYNOMIAL DECAY RATES FOR THE DAMPED WAVE EQUATION WITH HOLDER-LIKE DAMPING
Datchev, Kiril
Kleinhenz, Perry
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (08) : 3417 - 3425
[50] Asymptotic Profiles of Solutions for Structural Damped Wave Equations
Ikehata, Ryo
Takeda, Hiroshi
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2019, 31 (01) : 537 - 571

← 1 2 3 4 5 →