Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping

Abstract EN

In this paper, we study the existence of a global attractor for a class of n-dimension thermoelastic coupled beam equations with structural damping utt+Δ2u+Δ2ut-[σ(∫Ω(∇u)2dx)+ϕ(∫Ω∇u∇utdx)]Δu+f1(u)+g(ut)+νΔθ=q(x), in Ω×R+, and θt-Δθ+f2(θ)-νΔut=0.

Here Ω is a bounded domain of RN, and σ(·) and ϕ(·) are both continuous nonnegative nonlinear real functions and q is a static load.

The source terms f1(u) and f2(θ) and nonlinear external damping g(ut) are essentially |u|ρu, |θ|ϱθ, and |ut|rut respectively.