This paper deals with a high order viscoelastic wave equation with nonlinear boundary damping–source interactions. By the combination of Galerkin approximation and potential well methods, we obtain the global existence of weak solutions. Under some appropriate assumptions on the boundary damping–source terms and the relaxation function g, we establish general decay and blow-up results associated with solution energy. Estimates of the lifespan of solutions are also given.

中文翻译：

---

具有非线性边界阻尼和源项的粘弹性波动方程解的全局存在、不存在和衰减

本文涉及具有非线性边界阻尼-源相互作用的高阶粘弹性波动方程。通过Galerkin近似和势阱方法的结合，我们得到了弱解的全局存在性。在边界阻尼源项和弛豫函数 g 的一些适当假设下，我们建立了与溶液能量相关的一般衰减和膨胀结果。还给出了溶液寿命的估计值。