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arXiv · 1911.11432

Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping

Dandan Li·Qingquan Chang·Chunyou Sun
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Abstract

The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term $\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded domain $\Omega\subset\mathbb{R}^N$ with Dirichlet boundary conditions. Under some restrictions on $\beta(t)$ and critical growth restrictions on the nonlinear term $f$, we will prove the local and global well-posedness of the solution and derive the existence of a pullback attractor for the process associated with the degenerate damped hyperbolic problem.

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Dandan Li, Qingquan Chang, Chunyou Sun. 2019-11-26. Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping. https://arxiv.org/abs/1911.11432

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