Global attractor for a class of nonlinear lattices

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Abstract

We consider a class of nonlinear lattices with nonlinear damping(0.1)u¨n(t)+(1)pΔpun(t)+αun(t)+h(un(t))+g(n,u˙n(t))=fn, where nZ, tR+, α is a real positive constant, p is any positive integer and Δ is the discrete one-dimensional Laplace operator. Under suitable conditions on h and g we prove the existence of a global attractor for the continuous semigroup associated with (0.1). Our proofs are based on a difference inequality due to M. Nakao [M. Nakao, Global attractors for nonlinear wave equations with nonlinear dissipative terms, J. Differential Equations 227 (2006) 204–229].

Keywords

Nonlinear lattices
Global attractor
Nonlinear damping

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