Well-posedness and stability results for a class of nonlinear fourth-order wave equation with variable-exponents

نویسندگان
Ouaoua, Amar ID 1
Boughamsa, Wissem ID 2

1 Department of Sciences and Technology, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria

2 Department of Sciences and Technology, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria

doi
10.22075/ijnaa.2022.27129.3507
چکیده

In this paper, we consider a class of nonlinear fourth-order wave equation with damping and source terms of variable-exponent types. First, by the Faedo-Galerkin approximation method with positive initial energy and suitable conditions on the variable exponents $m(.)$ and $r(.) $, we established the local existence. We also prove that the local solution is global. Finally, the stability estimate of the solution was obtained by using the Komornik inequality

کلیدواژه‌ها
Nonlinear fourth-order wave equation, Faedo-Galerkin method, global existence, stability result