TiglayF072004.pdf (333.72 kB)
The Cauchy Problem for Two Nonlinear Evolution Equations
thesis
posted on 2004-07-08, 00:00 authored by Feride TiglayIn this work, we study the periodic Cauchy problem for two nonlinear evolution equations: The modified Hunter-Saxton equation and the Euler-Poisson equation. Modifying the techniques developed for Euler equations of hydrodynamics, we prove local well-posedness results in Sobolev spaces.
We also investigate the analytic regularity of solutions to these equations and prove Cauchy-Kowalevski type results.
Finally we describe the Hamiltonian structure of the Euler-Poisson equation on a semidirect product space.
History
Date Created
2004-07-08Date Modified
2018-10-08Defense Date
2004-06-25Research Director(s)
Joseph M. PowersCommittee Members
Gerard Misiolek Alex Himonas David P. Nicholls Pit-Mann WongDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Language
- English
Alternate Identifier
etd-07082004-114618Publisher
University of Notre DameProgram Name
- Mathematics
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