Y. Gao - J. G. Liu - X. Y. Lu - X. Xu
Maximal monotone operator in non-reflexive Banach space and the application to thin film equation in epitaxial growth on vicinal surface
Accepted Paper
Inserted: 19 apr 2017
Last Updated: 18 aug 2018
Journal: CVPDE
Year: 2017
Abstract:
In this work we consider \begin{equation}\label{abs} wt=(w_{hh}+c_0)^{-3}{hh},\qquad w(0)=w0, \end{equation} 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 $w_{hh}+c_0$.
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