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