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Asymptotic Stability of Biharmonic Shallow Water Equations


Abstract The dissipative shallow-water equations (SWE) possess both real-world application and extensive analysis in theoretical partial differential equations. This analysis is dominated by modeling the dissipation as diffusion, with its mathematical representation being the Laplacian. However, the usage of the biharmonic as a dissipative operator by oceanographers and atmospheric scientists and its underwhelming amount of analysis indicates a gap in SWE theory. In order to provide rigorous mathematical justification for the utilization of these equations in simulations with real-world implications, we extend an energy method utilized by Matsumura and Nishida for initial value problems relating to the equations of motion for compressible, vsicous, ... (more)
Created Date 2017-05
Contributor Kofroth, Collin Michael (Author) / Jones, Don (Thesis Director) / Smith, Hal (Committee Member) / School of Mathematical and Statistical Sciences / Barrett, The Honors College
Subject Mathematics / Partial Differential Equation Analysis / Fluid Dynamics
Series Academic Year 2016-2017
Type Text
Extent 50 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Collaborating Institutions Barrett, the Honors College
Additional Formats MODS / OAI Dublin Core / RIS


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