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 50 条

[1] Global well-posedness of the Cauchy problem for the 3D Jordan-Moore-Gibson-Thompson equation
Racke, Reinhard
Said-Houari, Belkacem
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2021, 23 (07)
[2] On the well-posedness and general decay results of Moore–Gibson–Thompson equation with memory
Hui Zhang
Zeitschrift für angewandte Mathematik und Physik, 2022, 73
[3] On the well-posedness and general decay results of Moore-Gibson-Thompson equation with memory
Zhang, Hui
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (06):
[4] GLOBAL WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE JORDAN-MOORE-GIBSON-THOMPSON EQUATION WITH ARBITRARILY LARGE HIGHER-ORDER SOBOLEV NORMS
Said-Houari, Belkacem
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2022, 42 (09) : 4615 - 4635
[5] WELL-POSEDNESS AND EXPONENTIAL DECAY OF THE ENERGY IN THE NONLINEAR JORDAN-MOORE-GIBSON-THOMPSON EQUATION ARISING IN HIGH INTENSITY ULTRASOUND
Kaltenbacher, Barbara
Lasiecka, Irena
Pospieszalska, Maria K.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2012, 22 (11):
[6] General Decay of the Cauchy Problem for a Moore–Gibson–Thompson Equation with Memory
Ilyes Lacheheb
Salim A. Messaoudi
Mediterranean Journal of Mathematics, 2021, 18
[7] Well-posedness and general decay for Moore–Gibson–Thompson equation in viscoelasticity with delay term
Abdelkader Braik
Abderrahmane Beniani
Khaled Zennir
Ricerche di Matematica, 2022, 71 : 689 - 710
[8] General Decay of the Cauchy Problem for a Moore-Gibson-Thompson Equation with Memory
Lacheheb, Ilyes
Messaoudi, Salim A.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (04)
[9] Well-posedness and general decay for Moore-Gibson-Thompson equation in viscoelasticity with delay term
Braik, Abdelkader
Beniani, Abderrahmane
Zennir, Khaled
RICERCHE DI MATEMATICA, 2022, 71 (02) : 689 - 710
[10] Inverse Problem for a Linearized Jordan-Moore-Gibson-Thompson Equation
Liu, Shitao
Triggiani, Roberto
NEW PROSPECTS IN DIRECT, INVERSE AND CONTROL PROBLEMS FOR EVOLUTION EQUATIONS, 2014, 10 : 305 - 351

← 1 2 3 4 5 →