Miloua, Attou A.
(2014)
Thin Film Equations With van der Waals Force.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
We are interested in the steady states of thin films in a cylindrical container with van der Waals forces which lead to a singular elliptic equation in a bounded domain with Neumann boundary conditions. Using the prescribed volume of the thin film as a variable parameter we investigated the structure of radial solutions and their associated energies using rigorous asymptotic analysis and numerical computation. Motivated by the existence of rupture solutions for thin film equations, we considered elliptic equations with more general non linearity and obtained sufficient condition for the existence of weak rupture solutions for a class of generalized elliptic equations. Finally such results can be generalized to a class of quasi-linear elliptic partial differential equations.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
29 May 2014 |
| Date Type: |
Publication |
| Defense Date: |
15 April 2014 |
| Approval Date: |
29 May 2014 |
| Submission Date: |
21 March 2014 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
81 |
| 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, point rupture solutions, elliptic equations, quasi-linear elliptic equations, asymptotic analysis |
| Date Deposited: |
29 May 2014 21:34 |
| Last Modified: |
15 Nov 2016 14:18 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/20782 |
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