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- Title
Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface.
- Authors
Gao, Yuan; Liu, Jian-Guo; Lu, Xin Yang; Xu, Xiangsheng
- Abstract
In this work we consider wt=whh+c0-3hh,w(0)=w0,<graphic></graphic>which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The mathematical difficulty is due to the fact that whh<inline-graphic></inline-graphic> can appear as a positive Radon measure. We prove the existence of a global strong solution with hidden singularity. In particular, (1) holds almost everywhere when whh<inline-graphic></inline-graphic> is replaced by its absolutely continuous part.
- Subjects
MONOTONE operators; OPERATOR theory; THIN films; HILBERT space; RADON measures
- Publication
Calculus of Variations & Partial Differential Equations, 2018, Vol 57, Issue 2, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-018-1326-x