General Decay and Well-Posedness of the Cauchy Problem for the Jordan-Moore-Gibson-Thompson Equation With Memory

被引：6

作者：

Boulaaras, Salah ^{[1
,2
]}

Chouch, Abdelbaki ^{[3
]}

Ouchenane, Djamel ^{[4
]}

机构：

[1] Qassim Univ, Coll Sci & Arts, Dept Math, Al Ras, Saudi Arabia

[2] Univ Oran 1, Lab Fundamental & Appl Math Oran LMFAO, Ahmed Benbella, Algeria

[3] Univ El Oued, Lab Operator Theory & PDEs Fdn & Applicat, Fac Exact Sci, Dept Math, Box 789, El Oued 39000, Algeria

[4] Amar Teledji Laghouat Univ, Lab Pure & Appl Math, Laghouat, Algeria

来源：

FILOMAT | 2021年 / 35卷 / 05期

关键词：

Jordan-Moore-Gibson-Thompson (JMGT); General decay; Memory term; Relaxation function;

D O I：

10.2298/FIL2105745B

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan-Moore-Gibson-Thompson (JMGT) equation with the presence of both memory. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result, and we show a local existence result in appropriate function spaces. Finally, we prove a global existence result for small data, and we prove the uniqueness of the generalized solution.

引用

页码：1745 / 1773

页数：29

共 41 条

[31] Well-posedness and decay property of regularity-loss type for the Cauchy problem of the standard linear solid model with Gurtin-Pipkin thermal law [J].

Wang, Danhua ;

Liu, Wenjun .

ASYMPTOTIC ANALYSIS, 2021, 123 (1-2) :181-201

[32] Well-posedness and dynamics for the von Karman equation with memory and nonlinear time-varying delay [J].

Cui, Xiaona ;

Li, Ke .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (14) :15481-15505

[33] WELL-POSEDNESS AND STABILITY FOR AN ABSTRACT EVOLUTION EQUATION WITH HISTORY MEMORY AND TIME DELAY IN HILBERT SPACE [J].

Chellaoua, Houria ;

Boukhatem, Yamna ;

Feng, Baowei .

ADVANCES IN DIFFERENTIAL EQUATIONS, 2023, 28 (11-12) :953-980

[34] WELL-POSEDNESS AND ENERGY DECAY OF A TRANSMISSION PROBLEM OF KIRCHHOFF TYPE WAVE EQUATIONS WITH DAMPING AND DELAY TERMS [J].

Liu, Zhiqing ;

Gao, Cunchen ;

Fang, Zhong Bo .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, :1-23

[35] Well-Posedness and General Decay for Nonlinear Damped Porous Thermoelastic System with Second Sound and Distributed Delay Terms [J].

Ouchenane, Djamel ;

Zennir, Khaled ;

Guidad, Derradji .

JOURNAL OF APPLIED NONLINEAR DYNAMICS, 2022, 11 (01) :153-170

[36] Well-posedness and general energy decay of solutions for a nonlinear damping piezoelectric beams system with thermal and magnetic effects [J].

Messaoudi, Hassan ;

Ardjouni, Abdelouaheb ;

Zitouni, Salah ;

Khochemane, Houssem Eddine .

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2023, 52 (06) :1615-1630

[37] Global well-posedness and general energy decay of solutions for fully dynamic and electrostatic piezoelectric beams with a viscoelastic damping [J].

Messaoudi, Hassan ;

Douib, Madani ;

Zitouni, Salah .

FILOMAT, 2024, 38 (27) :9475-9492

[38] Well posedness and general decay for a wave equation with logarithmic source term and distributed delay of fractional type [J].

Choucha, Abdelbaki ;

Boulaaras, Salah ;

Rouhani, Behzad Djafari .

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2025, 16 (03)

[39] Well-posedness and general energy decay for a nonlinear piezoelectric beams system with magnetic and thermal effects in the presence of distributed delay [J].

Messaoudi, Hassan ;

Douib, Madani ;

Zitouni, Salah .

JOURNAL OF THERMAL STRESSES, 2024, 47 (05) :652-671

[40] Well-posedness and energy decay for Timoshenko systems with discrete time delay under frictional damping and/or infinite memory in the displacement [J].

Guesmia A. .

Afrika Matematika, 2017, 28 (7-8) :1253-1284

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