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Global attractor for a model of extensible beam with nonlinear damping and source terms

机译:具有非线性阻尼和源项的可扩展梁模型的整体吸引子

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摘要

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, utt+Δ2u-M(∫Ω|?u|2dx)Δu+f(u)+g(ut)= hinΩ×R+, where Ω is a bounded domain of RN, M is a nonnegative real function and h∈L2(Ω). The nonlinearities f(u) and g(ut) are essentially |u|ρu-|u|σu and |ut|rut respectively, with ρ,σ,r>0 and σ<ρ. This kind of problem models vibrations of extensible beams and plates.
机译:本文关注的是非线性梁方程的整体吸引子的存在,具有非线性阻尼和源项utt +Δ2u-M(∫Ω|?u | 2dx)Δu+ f(u)+ g(ut)= hinΩ×R +,其中Ω是RN的有界域,M是非负实函数,h∈L2(Ω)。非线性f(u)和g(ut)本质上分别为| u |ρu-| u |σu和| ut | rut,其中ρ,σ,r> 0并且σ<ρ。这种问题模拟了可伸长梁和板的振动。

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