ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR LINEAR EVOLUTIONARY BOUNDARY VALUE PROBLEM OF VISCOELASTIC DAMPED WAVE EQUATION

被引：2

作者：

Berbiche, Mohamed ^{[1
]}

机构：

[1] Univ Med Khider, Dept Math, POB 145, Biskra 07000, Algeria

来源：

MATHEMATICA BOHEMICA | 2020年 / 145卷 / 02期

关键词：

global existence; uniqueness; uniform stabilization; ENERGY DECAY; ELECTROMAGNETIC SYSTEMS; MEMORY; STABILITY; THERMODYNAMICS; STABILIZATION; CONVERGENCE;

D O I：

10.21136/MB.2019.0054-18

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence of global in time and uniform decay of weak solutions to the initial-boundary value problem related to the dynamic behavior of evolution equation accounting for rotational inertial forces along with a linear nonlocal frictional damping arises in viscoelastic materials. By constructing appropriate Lyapunov functional, we show the solution converges to the equilibrium state polynomially in the energy space.

引用

页码：205 / 223

页数：19

共 28 条

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

Aassila, M ;

Cavalcanti, MM ;

Soriano, JA .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (05) :1581-1602

[2] The Euler-Bernoulli beam equation with boundary dissipation of fractional derivative type [J].

Achouri, Zineb ;

Amroun, Nour Eddine ;

Benaissa, Abbes .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (11) :3837-3854

[3]

Aizicovici S, 2001, Journal of Evolution Equations, V1, P69

[4] Frictional versus viscoelastic damping in a semilinear wave equation [J].

Cavalcanti, MM ;

Oquendo, HP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2003, 42 (04) :1310-1324

[5] Convergence to steady states of solutions of semilinear evolutionary integral equations [J].

Chill, R ;

Fasangová, E .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2005, 22 (03) :321-342

[6] THERMODYNAMICS OF ELECTROMAGNETIC FIELDS IN MATERIALS WITH MEMORY [J].

COLEMAN, BD ;

DILL, EH .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1971, 41 (02) :132-&

[7] THERMODYNAMIC RESTRICTIONS ON CONSTITUTIVE EQUATIONS OF ELECTROMAGNETIC THEORY [J].

COLEMAN, BD ;

DILL, EH .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1971, 22 (04) :691-&

[8]

DAFERMOS CM, 1970, ARCH RATION MECH AN, V37, P297

[9] Stabilization through viscoelastic boundary damping: a semigroup approach [J].

Desch, W. ;

Fasangova, E. ;

Milota, J. ;

Propst, G. .

SEMIGROUP FORUM, 2010, 80 (03) :405-415

[10] Thermodynamics of electromagnetic isothermal systems with memory [J].

Fabrizio, M ;

Morro, A .

JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS, 1997, 22 (02) :110-128

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