The paper deals with the existence of a global solution of a singular one‐dimensional viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized frictional damping a(x)u_t using the potential well theory. Furthermore, the general decay result is proved. We construct a suitable Lyapunov functional and make use of the perturbed energy method.

中文翻译：

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具有非线性源项，非局部边界条件和局部阻尼项的奇异非局部粘弹性系统解的整体存在和衰减

用单数的一维粘弹性系统的具有非线性源项，非局部边界条件的全局解决方案存在的纸交易，和局部摩擦阻尼一个（X）Ü_吨使用势阱理论。此外，证明了一般的衰减结果。我们构造了一个合适的Lyapunov函数，并利用了扰动能量法。