Global existence uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation

Asymptiotic Behavior for the Viscoelastic Kirchhoff Type Equation With an Internal Time-Varying Delay Term

“…By using Galerkin's approximation and a routine procedure similar to that of cite [4,15], we can the global existence result for the solution subject to (1)- (4) (4) with the above all conditions. We define the Kirchhoff type energy functional E(t) as…”

“…Our purpose is focused on not only memory effects but also time-varying delay for the problem otherwise the previous result [3]. Recently, problems with Timoshenko or basic hyperbolic type for viscoelastic materials have been considered by many authors (See [4,5]). Besides, many engineering devices involve the transverse vibration of axially moving strings.…”

Stabilization of an axially moving viscoelastic string under a spatiotemporally varying tension

“…Proof The proof is based on the Galerkin approximation method, that can be adapted, eg, from Li et al □…”

A New Approach to the Existence of Quasiperiodic Solutions for Second-Order Asymmetric p-Laplacian Differential Equations

“…In recent years, all kinds of nonlinear dynamic behavior, such as the existence of positive solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and signchanging solutions [17,18], the existence and uniqueness of solutions [19][20][21][22][23][24][25], the existence and multiplicity results [26][27][28][29][30], and the existence of unbounded solutions [31,32], have been widely investigated for some nonlinear ordinary differential equations and partial differential equations due to the application in many fields such as physics, mechanics, and the engineering technique fields. In the present paper, we deal with the existence of Aubry-Mather sets and quasiperiodic solutions for the second-order differential equations with a -Laplacian and an asymmetric nonlinear term…”