dc.contributor.advisor Deconinck, Bernard en_US dc.contributor.author Vasan, Vishal en_US dc.date.accessioned 2012-09-13T17:31:29Z dc.date.available 2012-09-13T17:31:29Z dc.date.issued 2012-09-13 dc.date.submitted 2012 en_US dc.identifier.other Vasan_washington_0250E_10437.pdf en_US dc.identifier.uri http://hdl.handle.net/1773/20723 dc.description Thesis (Ph.D.)--University of Washington, 2012 en_US dc.description.abstract Euler's equations describe the evolution of waves on the surface of an ideal incompressible fluid. In this dissertation, I discuss some boundary-value problems associated with Euler's equations. My approach is motivated by the ideas generated by Fokas and collaborators, particularly the notion of a global relation for boundary-value problems for partial differential equations. I introduce a new method to compute the evolution of the free surface of a water wave based on a reinterpretation of the relevant global relation. Next I consider the bathymetry reconstruction problem i.e.<\italic>, the reconstruction of the bottom boundary of a fluid from measurements of the free-surface elevation alone. By analyzing the global relation for the water-wave problem, I derive an exact, fully nonlinear equation which is solved for the bottom boundary. Finally, I present a method of reconstructing the free surface of a water wave using measurements of the pressure at the bottom boundary. Using this reconstruction, I obtain several new asymptotic approximations of the surface elevation in terms of the pressure at the bottom. Comparisons with numerical and experimental data show excellent agreement with my predicted reconstructions. en_US dc.format.mimetype application/pdf en_US dc.language.iso en_US en_US dc.rights Copyright is held by the individual authors. en_US dc.subject Boundary-value problems; Inverse problems; Water waves en_US dc.subject.other Applied mathematics en_US dc.subject.other Mathematics en_US dc.subject.other Applied mathematics en_US dc.title Some Boundary-Value Problems for Water Waves en_US dc.type Thesis en_US dc.embargo.terms No embargo en_US
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