This work deals with a class of nonlinear viscoelastic wave equations with strong damping and variable exponent sources. The main interest of this paper compared to many previous works in the literature is able to use the idea of potential well method to study both the finite time blow-up for solutions starting from the unstable sets and decay estimate for global solutions starting in the potential wells.

中文翻译：

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具有可变源的粘弹性方程的指数衰减和膨胀结果

这项工作涉及一类具有强阻尼和可变指数源的非线性粘弹性波动方程。与文献中的许多先前工作相比，本文的主要兴趣在于能够使用势井法的思想来研究从不稳定集开始的解的有限时间爆破和从势井开始的全局解的衰减估计井。