The present article is concerned with a class of corner-degenerate viscoelastic higher hyperbolic equations with nonlinear damping and boundary source terms. First, we prove some invariance results about the energy functional and the solution set of our problem by using potential wells methods on the manifolds with corner singularity. Then, we establish existence results of global weak solution on the corner Sobolev space with the suitable weight data and appropriate assumptions on the initial-boundary data.

中文翻译：

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具有非线性阻尼和源项的拐角奇异性粘弹性方程的不变性和存在性分析

本文关注一类具有非线性阻尼和边界源项的角退化粘弹性高双曲方程。首先，我们通过在具有拐角奇异性的流形上使用势阱方法证明了关于能量泛函和问题的解集的一些不变性结果。然后，我们利用合适的权重数据和对初始边界数据的适当假设，建立了拐角 Sobolev 空间上全局弱解的存在性结果。