On the steady states of thin film equations

liu, guoqing (2015) On the steady states of thin film equations. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

This dissertation studies the steady state of thin film type equations. Different considerations of physical forces give different formulations of differential equations. We start with generalized thin film evolution and derive the second order elliptic equation for steady states.
For the thin film driven by both van der Waals force and Born repulsion force, we define associated energy and obtain a classical energy minimizing problem by taking semi-limit. The solution has been proven to converge to a Dirac measure in the limit that repulsive force term tends to $0$. Asymptotic analysis show that the location of the spike would be a point on the boundary with maximal curvature.
Furthermore, we neglect the Born repulsion force and study radial steady state solution for van der Waals force driven thin film equation. We link the volume constraint problem with a initial value ordinary different equation and analyze how radial steady state solution and associated energy depend on the average thickness.

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Details

Item Type:	University of Pittsburgh ETD
Status:	Unpublished
Creators/Authors:	Creators Email Pitt Username ORCID liu, guoqing gul8@pitt.edu GUL8
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee Chair Jiang, Huiqiang hqjiang@pitt.edu HQJIANG Committee CoChair Chen, Xinfu xinfu@pitt.edu XINFU Committee Member Lewicka, Marta lewicka@pitt.edu LEWICKA Committee Member Splecev, Dejan slepcev@math.cmu.edu Committee Member Chen, Ming mingchen@pitt.edu MINGCHEN
Date:	22 June 2015
Date Type:	Publication
Defense Date:	15 April 2015
Approval Date:	22 June 2015
Submission Date:	17 April 2015
Access Restriction:	No restriction; Release the ETD for access worldwide immediately.
Number of Pages:	101
Institution:	University of Pittsburgh
Schools and Programs:	Dietrich School of Arts and Sciences > Mathematics
Degree:	PhD - Doctor of Philosophy
Thesis Type:	Doctoral Dissertation
Refereed:	Yes
Uncontrolled Keywords:	Thin Film Equations, Dirac Measure, Maximal Curvature, Van der Waals force, Radial Steady States
Date Deposited:	22 Jun 2015 13:28
Last Modified:	15 Nov 2016 14:27
URI:	http://d-scholarship.pitt.edu/id/eprint/24822

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