Invariance and existence analysis of viscoelastic equations with nonlinear damping and source terms on corner singularity

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.