Hyperbolic Relaxation of a Fourth Order Evolution Equation

Abstract

We propose a hyperbolic relaxation of a fourth order evolution equation, with an inertial term $\eta u_{tt}$, where $\eta \in (0,1]$. We prove the existence of several absorbing sets having different regularities and the existence of a global attractor that is bounded in $H^4(I)\times \{H^2(I)\cap H_0^1(I)\}$.