Calculus of Variations and Geometric Measure Theory
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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

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


Accepted Paper

Inserted: 19 apr 2017
Last Updated: 18 aug 2018

Journal: CVPDE
Year: 2017


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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