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

Authors : Morteza Koozehgar Kalleji

Pages : 1085-1101

Doi:10.15672/hujms.1286267

View : 86 | Download : 170

Publication Date : 2024-08-27

Article Type : Research Paper

Abstract :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 $\\mathbb{M}$ with corner singularities. We prove that, under certain conditions on relaxation function $g$, any solution $u$ in the corner-Sobolev space $\\mathcal{H}^{1,(\\frac{N-1}{2},\\frac{N}{2})}_{\\partial^{0}\\mathbb{M}}(\\mathbb{M})$ blows up in finite time. The estimates of the life-span of solutions are also given.
Keywords : higher order hyperbolic viscoelastic equations, singular potential wells of higher order hyperbolic, corner Sobolev space, singularities, blow up