Optimal decay for a wave transmission problem with fading memory

被引：2

作者：

Liu, Zhiqing ^{[1
]}

Fang, Zhong Bo ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao, Peoples R China

来源：

APPLICABLE ANALYSIS | 2022年 / 101卷 / 06期

基金：

中国国家自然科学基金;

关键词：

S; Hansen; transmission problem; time-varying delay; boundary memory source; general decay; optimal decay; TIME DELAYS; BOUNDARY; STABILIZATION; EQUATION; STABILITY; SYSTEMS;

D O I：

10.1080/00036811.2020.1798413

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The transmission of waves over a body composed of two different materials are considered in this paper. One component is a simple elastic part while the other is a viscoelastic component with time-varying delay and damping effect. Besides, one part of the boundary is controlled by a nonlinear memory source term while the other part of the boundary is clamped. Under the influence of time-varying delay and damping effect, we derive a general decay estimate of the energy when the internal viscoelastic memory and the boundary memory decay simultaneously. Moreover, we present some examples to illustrate that the decay rate of the energy is optimal in some range of decay exponent of the memory.

引用

页码：1984 / 2007

页数：24

共 22 条

[1] Alabau Boussouira F, 2008, J FUNCT ANAL, V254
[2] Alabau Boussouira F, 2009, C R MATH, V347
[3] Uniform stabilization for the transmission problem of the Timoshenko system with memory
Alves, Margareth S.
Raposo, Carlos Alberto
Munoz Rivera, Jaime E.
Sepulveda, Mauricio
Vera Villagran, Octavio
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (01) : 323 - 345
[4] Andrade D, 2006, ELECTRON J DIFFER EQ
[5] Bastos WD, 2007, ELECTRON J DIFFER EQ
[6] Benseghir A, 2014, ELECTRON J DIFFER EQ
[7] Existence and uniform decay of solutions of a degenerate equation with nonlinear boundary damping and boundary memory source term
Cavalcanti, MM
Cavalcanti, VND
Prates, JS
Soriano, JA
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 38 (03) : 281 - 294
[8] NOT ALL FEEDBACK STABILIZED HYPERBOLIC SYSTEMS ARE ROBUST WITH RESPECT TO SMALL TIME DELAYS IN THEIR FEEDBACKS
DATKO, R
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1988, 26 (03) : 697 - 713
[9] AN EXAMPLE ON THE EFFECT OF TIME DELAYS IN BOUNDARY FEEDBACK STABILIZATION OF WAVE-EQUATIONS
DATKO, R
LAGNESE, J
POLIS, MP
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1986, 24 (01) : 152 - 156
[10] Fabrizio M., 2002, Appl. Analysis, V81, P1245, DOI [10.1080/0003681021000035588, DOI 10.1080/0003681021000035588]

← 1 2 3 →