# Maximal monotone operator in non-reflexive Banach space and the application to thin film equation in epitaxial growth on vicinal surface

created by lu on 19 Apr 2017
modified on 18 Aug 2018

[BibTeX]

Accepted Paper

Inserted: 19 apr 2017
Last Updated: 18 aug 2018

Journal: CVPDE
Year: 2017

Abstract:

In this work we consider \label{abs} wt=(w_{hh}+c_0)^{-3}{hh},\qquad w(0)=w0, which is derived from thin film equation for epitaxial growth on vicinal surface. We establish a general structure for abstract evolution equation with maximal monotone operator in non-reflexive Banach space which can be used in a wide class of degenerate parabolic equations. Following this structure, we formulate a global strong solution to \eqref{abs} which allows a Radon measure occurring. Then we prove the existence of such a global strong solution and obtain the almost everywhere positivity of $w_{hh}+c_0$.