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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Well-Posedness and Regularity for a Higher Order Periodic Mkdv Equation.

Well-Posedness and Regularity for a Higher Order Periodic Mkdv Equation.

Schlotthauer-Hannah, Heather

Paperback

General Mathematics

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ISBN10: 124375320X
ISBN13: 9781243753205
Publisher: Proquest Umi Dissertation Pub
Pages: 104
Weight: 0.44
Height: 0.22 Width: 7.44 Depth: 9.69
Language: English
We 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 >= 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.

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