Global well-posedness of solutions for the epitaxy thin film growth model

Ning Duan,Xiaopeng Zhao,Fengnan Liu

doi:10.15388/namc.2021.26.23936

Abstract

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.

Highlights

There have been several experimental studies exhibiting a novel type of the epitaxial growth of nanoscale thin films
On the basis of the above figures, we find out that the solutions to problems (11) and (12) tend to be stable as long as the time goes on, which means that the results on global existence of solutions for the epitaxy thin film growth model are reasonable
We study a continuum model of YBCO film growth, which accounts for nucleation and the transition to island growth, as well as for the subsequent roughening and coarsening of the surface profile

Summary

Introduction

There have been several experimental studies exhibiting a novel type of the epitaxial growth of nanoscale thin films. It will not be used in the proofs of the main results of this paper, one would like to point out that Eq (5) can be represented as the gradient flow of the following energy functional which means This fact was employed in [2, 10, 23] to study the thin film equation. We consider the small initial data global existence and uniqueness of solutions for the following initial-boundary value problem:. The main purpose of this paper is to study the global well-posedness of solutions for problem (7). The last section illustrates the qualitative behavior of the constructed approximate solution to problem (7) through some numerical simulations

Preliminaries

Proof of Theorem 1

Numerical experiments

Conclusion