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Type of Document Dissertation Author Tiglay, Feride URN etd-07082004-114618 Title THE CAUCHY PROBLEM FOR TWO NONLINEAR EVOLUTION EQUATIONS Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Joseph M. Powers Committee Chair Alex Himonas Committee Member David P. Nicholls Committee Member Gerard Misiolek Committee Member Pit-Mann Wong Committee Member Keywords
- PDE
- initial value problems
- bihamiltonian
- mathematical physics
Date of Defense 2004-06-25 Availability unrestricted Abstract In 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.
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