论文标题
良好的亮度和强大的吸引子，用于具有退化非局部强阻尼的光束模型
Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping
论文作者
论文摘要
This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in $Ω\subset\mathbb{R}^n$: $u_{tt}-κΔu+Δ^2u-γ(\Vert Δu\Vert^2+\Vert u_t \ vert^2）^qΔu_t+f（u）= 0 $。我们证明了薄弱解决方案的全球存在和独特性，这对[24]中的一个开放问题给出了积极的答案。此外，我们为相应的弱解决方案半群建立了强大的吸引子，其中``强度''意味着吸引子的紧凑性和吸引力是更强的空间$ \ MATHCAL {h} _ {h} _ {\ frac {\ frac {1}} {q}}} $。
This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in $Ω\subset\mathbb{R}^n$: $u_{tt}-κΔu+Δ^2u-γ(\Vert Δu\Vert^2+\Vert u_t\Vert^2)^qΔu_t+f(u)=0$. 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 $\mathcal{H}_{\frac{1}{q}}$.
