Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping

2022/11/01 by Senlin Yan, Yan, Senlin, Chengkui Zhong +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2211.00287

openalex publication_date 2022/11/01 · openalex created_date 2022/11/07 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in Ω⊂ℝⁿ: u_tt-κΔu+Δ²u-γ(\Vert Δu\Vert²+\Vert u_t\Vert²)^qΔu_t+f(u)=0. We prove the global existence and uniqueness of weak solutions, which gives a positive answer to an open question in [24]. Moreover, we establish the existence of a strong attractor for the corresponding weak solution semigroup, where the ``strong" means that the compactness and attractiveness of the attractor are in the topology of a stronger space H_(1)/(q).

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