Decay estimate and blow-up for a fourth order parabolic equation modeling epitaxial thin film growth

Abstract

In this paper, we study a fourth order parabolic equation modeling epitaxial thin film growth. By using the potential well method and some inequality techniques, we obtain the decay estimate of weak solutions. Meanwhile, the blow-up time is estimated from above and below. The blow-up rate is also derived.

Keywords

• parabolic equation
• epitaxial thin film growth
• decay estimate
• blow-up