Mohebbi, Mahdi
(2013)
Time-periodic solutions of magnetoelastic systems and embedding of the attractor of 2-dimensional Navier-Stokes equations into Euclidean spaces.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
In this work we address two rather independent problems. The first part is dedicated to the existence of periodic solutions for a magnetoelastic system modeling the interaction of a linear elastic body with a nonlinear dissipation and a magnetic field. The resulting system is a coupled Hyperbolic-Parabolic system of PDE’s.
In the second part, for 2-D Navier-Stokes equations on a C2 bounded domain Ω and a time independent force f, a class of nonlinear homeomorphisms is constructed from the attractor of Navier-Stokes to curves in RN, for sufficiently large N. The construction uses an ε-net on Ω (so does not use the information “near” the boundary) and is more physically perceivable compared to abstract common embeddings.
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Details
Item Type: |
University of Pittsburgh ETD
|
Status: |
Unpublished |
Creators/Authors: |
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ETD Committee: |
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Date: |
28 June 2013 |
Date Type: |
Publication |
Defense Date: |
4 April 2012 |
Approval Date: |
28 June 2013 |
Submission Date: |
27 March 2013 |
Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
Number of Pages: |
70 |
Institution: |
University of Pittsburgh |
Schools and Programs: |
Swanson School of Engineering > Mechanical Engineering |
Degree: |
PhD - Doctor of Philosophy |
Thesis Type: |
Doctoral Dissertation |
Refereed: |
Yes |
Uncontrolled Keywords: |
Attractors, Dynamic Systems, Navier-Stokes Equations, Magnetoelasticity, Periodic Solutions, Hyperbolic-Parabolic Systems |
Date Deposited: |
28 Jun 2013 20:15 |
Last Modified: |
15 Nov 2016 14:10 |
URI: |
http://d-scholarship.pitt.edu/id/eprint/17956 |
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