Strong solutions to a fourth order exponential PDE describing epitaxial growth

Abstract

In this paper we prove the global existence of a strong solution to the initial boundary value problem for the exponential partial differential equation ∂tu−Δe−Δu+e−Δu−1=0. The equation was proposed as a continuum model for epitaxial growth of crystal surfaces on vicinal surfaces with evaporation and deposition effects [6]. Our investigations reveal that we must control the size of both ‖e−Δu(x,0)‖W2,2(Ω) and ‖eΔu(x,0)‖∞,Ω suitably to achieve our results. Related results in [8,10] were established via the Weiner algebra framework. Here we offer a totally new approach, which seems to shed more light on the nature of exponential nonlinearity.