Finite-time property of a mechanical viscoelastic system with nonlinear boundary conditions on corner-Sobolev spaces

In this article, we deal with the initial boundary value problem for a viscoelastic system related to the quasilinear parabolic equation with nonlinear boundary source term on a manifold M with corner singularities. We prove that, under certain conditions on relaxation function g, any solution u in the corner-Sobolev space H1,(N-1/2,N/2)_∂⁰M(M) blows up in finite time. The estimates of the life-span of solutions are also given.