Global well-posedness of solutions for the epitaxy thin film growth model - Duan, Ning; Liu, Fengnan; Zhao, Xiaopeng (Nonlinear Analysis: Modelling and Control, 2021)
In this paper, we consider the global well-posedness of solutions for the initial-boundary value problems of the epitaxy growth model. We first construct the local smooth solution, then by combining some a priori estimates, continuity argument, the local smooth solutions are extended step by step to all t > 0, provided that the initial datums sufficiently small and the smooth nonlinear functions satisfy certain local growth conditions.