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

Year 2024, Volume: 53 Issue: 4, 1085 - 1101, 27.08.2024

Morteza Koozehgar Kalleji

https://doi.org/10.15672/hujms.1286267

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

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