Well-posedness and stability results for some nonautonomous abstract linear hyperbolic equations with memory

被引：4

作者：

Al-Khulaifi, Waled ^{[1
]}

Diagana, Toka ^{[2
]}

Guesmia, Aissa ^{[3
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, POB 546, Dhahran 31261, Saudi Arabia

[2] Univ Alabama, Dept Math Sci, 301 Sparkman Dr, Huntsville, AL 35899 USA

[3] Univ Lorraine, Inst Elie Cartan Lorraine, UMR 7502, 3 Rue Augustin Fresnel,BP 45112, F-57073 Metz 03, France

来源：

SEMIGROUP FORUM | 2022年 / 105卷 / 02期

关键词：

Well-posedness; Asymptotic behavior; Self-adjoint; Infinite memory; Evolution families; Nonautonomous evolution equations; Nonautonomous petrovsky type equation; Nonautonomous wave equation; ASYMPTOTIC STABILITY; GENERAL DECAY; VISCOELASTIC EQUATION; EXPONENTIAL STABILITY; WAVE-EQUATION; INTEGRODIFFERENTIAL EQUATIONS; DISSIPATIVE SYSTEMS; INFINITE MEMORY; EXISTENCE; SEMIGROUPS;

D O I：

10.1007/s00233-022-10284-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study a class of second-order abstract linear hyperbolic equations with infinite memory that involve time-dependent unbounded linear operators. We obtain the well-posedness and stability of solutions to those nonautonomous second-order evolution equations under some appropriate assumptions. Our results generalize a number of previously known results in the autonomous case. Some specific examples are given to illustrate our abstract results, such as the nonautonomous Petrovsky type and wave equations.

引用

页码：351 / 373

页数：23

共 46 条

[1] Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain [J].