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

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

کلیدواژه ها:

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