Decay result in a problem of a nonlinearly damped wave equation with variable exponent

AIMS Mathematics

Mohammad Kafini¹  Jamilu Hashim Hassan²  Mohammad M. Al-Gharabli³ 

[1] 1. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia3. The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;1. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;2. The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3. The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;

关键词: viscoelasticity;    relaxation function;    general decay;    logarithmic nonlinearity;    variable exponent;   

DOI  :  10.3934/math.2022170

来源: DOAJ

【 摘 要 】

In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.

【 授权许可】

Unknown