General decay result for the wave equation with memory and acoustic boundary conditions

被引：8

作者：

Yoon, Min ^{[1
]}

Lee, Mi Jin ^{[2
]}

Kang, Jum-Ran ^{[1
]}

机构：

[1] Pukyong Natl Univ, Dept Appl Math, Busan 48513, South Korea

[2] Pusan Natl Univ, Dept Math, Busan 46241, South Korea

来源：

APPLIED MATHEMATICS LETTERS | 2023年 / 135卷

基金：

新加坡国家研究基金会;

关键词：

Optimal decay; Viscoelastic wave equation; Acoustic boundary conditions; ENERGY; RATES;

D O I：

10.1016/j.aml.2022.108385

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the energy decay rates for the viscoelastic wave equation with acoustic boundary conditions. Here we consider with minimal conditions on the L-1(0,infinity) relaxation function alpha, namely alpha '(t) <= -zeta(t)G(alpha(t)), where G is an increasing and convex function near the origin and zeta is a nonincreasing function. Using the assumptions on the relaxation function alpha due to Mustafa (2018), we generalize the work of Park and Park (2011) and Liu (2014) to general decay. (C) 2022 Elsevier Ltd. All rights reserved.

引用

页数：7

共 11 条

[1] A general method for proving sharp energy decay rates for memory-dissipative evolution equations
Alabau-Boussouira, Fatiha
Cannarsa, Piermarco
[J]. COMPTES RENDUS MATHEMATIQUE, 2009, 347 (15-16) : 867 - 872
[2] Arnold V. I., 1989, GRAD TEXTS MATH, V60, DOI 10.1007/978-1-4757-2063-1
[3] ACOUSTIC BOUNDARY-CONDITIONS
BEALE, JT
ROSENCRA.SI
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 80 (06) : 1276 - 1278
[4] General decay rate for a class of weakly dissipative second-order systems with memory
Hassan, Jamilu Hashim
Messaoudi, Salim A.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (08) : 2842 - 2853
[5] Coupled second order evolution equations with fading memory: Optimal energy decay rate
Jin, Kun-Peng
Liang, Jin
Xiao, Ti-Jun
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (05) : 1501 - 1528
[6] Arbitrary rate of decay for a viscoelastic equation with acoustic boundary conditions
Liu, Wenjun
[J]. APPLIED MATHEMATICS LETTERS, 2014, 38 : 155 - 161
[7] General decay of solutions for a weak viscoelastic equation with acoustic boundary conditions
Liu, Wenjun
Sun, Yun
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2014, 65 (01): : 125 - 134
[8] Optimal decay rates for the viscoelastic wave equation
Mustafa, Muhammad I.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (01) : 192 - 204
[9] General decay result for nonlinear viscoelastic equations
Mustafa, Muhammad I.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 457 (01) : 134 - 152
[10] Decay rate estimates for wave equations of memory type with acoustic boundary conditions
Park, Jong Yeoul
Park, Sun Hye
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (03) : 993 - 998

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