This work is devoted to studying a wave equation with degenerate nonlocal nonlinear damping and source terms. By potential well theory, we show the asymptotic stability of energy in the presence of a degenerate damping of polynomial type when the initial energy is small. Also, we firstly derive some sufficient conditions on initial data which lead to finite time blow-up.

中文翻译：

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具有退化非局部非线性阻尼和源项的波动方程的渐近稳定性和爆破

这项工作致力于研究具有退化非局部非线性阻尼和源项的波动方程。通过势阱理论，我们证明了当初始能量较小时，存在多项式退化阻尼时能量的渐近稳定性。此外，我们首先在初始数据上推导出一些导致有限时间爆炸的充分条件。