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Well-Posedness and Regularity for a Higher OrderPeriodic Mkdv Equation
thesis
posted on 2007-04-20, 00:00 authored by Heather Dawn Schlotthauer-HannahWe consider the higher order mKdV equation, so that we are examining those equations with a higher dispersion term of the order m, where m is odd and larger than 3. The corresponding periodic Cauchy problem is in fact well-posed in Sobolev spaces for all s ge 1/2. We then show that the solution to the periodic Cauchy problem for this higher order equation with analytic initial data is analytic in the space variable x at any fixed time t near time zero. However, while this analyticity is not guaranteed in t, the solution does have Gevrey-m regularity with respect to the time variable t.
History
Date Created
2007-04-20Date Modified
2018-10-05Defense Date
2007-03-22Research Director(s)
Alex HimonasCommittee Members
Alex HimonasDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Language
- English
Alternate Identifier
etd-04202007-135742Publisher
University of Notre DameProgram Name
- Mathematics
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