Global attractor for hyperbolic equation with nonlinear damping and linear memory

Abstract

In this paper, we study the existence of global attractors for the hyperbolic equation with nonlinear damping and linear memory. Keywordsglobal attractor, absorbing set, asymptotically a priori estimate, nonlinear damping, viscoelasticity MSC(2000): 35B40, 35B41Citation: Park J Y, Kang J R. Global attractor for hyperbolic equation with nonlinear damping and linear memory.

Long‐time behavior of a nonlinear viscoelastic beam equation with past history

“…Giorgi et al studied the existence of a global attractor to the following viscoelastic wave equation The existence of a global attractors for () by introducing a linear damping u t was proved by Ma and Zhong . Further, Park and Kang considered the same results on the Equation () with a nonlinear damping g ( u t ).…”

Long-time behavior of a suspension bridge equations with past history

“…Later, Park and Kang [19] generalized the results of [7]. By adapting a classical argument by Dafermos [5], they studied the global attractor of semi-linear hyperbolic equation with linear memory and nonlinear damping.…”

Global attractor for suspension bridge equations with memory

“…In recent years, the asymptotic behavior of evolution equations with memory effects have been studied by many authors (see, and references therein). In order to construct a dynamical system corresponding to a model with memory, they use the so‐called history space setting, which was proposed by Dafermos .…”

“…The main purpose of this work is to study the long-time dynamics for a system related to suspension bridge equations with memory In recent years, the asymptotic behavior of evolution equations with memory effects have been studied by many authors (see, [11][12][13][14][15][16][17][18][19] and references therein). In order to construct a dynamical system corresponding to a model with memory, they use the so-called history space setting, which was proposed by Dafermos [11].…”

“…Giorgi et al [14] and Ma and Zhong [15] studied the global attractor of semi-linear hyperbolic equation with linear memory. Later, Park and Kang [16] generalized the results of [13][14][15]. Jorge Silva and Ma [17,18] proved the exponential stability and global attractor of plate equations with memory and perturbation of p-Laplacian type.…”