Continuity Properties of the Solution Map for the Generalized Reduced Ostrovsky Equation

Doctoral Dissertation
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Abstract

It is shown that the data-to-solution map for the generalized reduced Ostrovsky (gRO) equation is not uniformly continuous on bounded sets in Sobolev spaces on the circle with exponent s > 3/2. Considering that for this range of exponents the gRO equation is well-posed with continuous dependence on initial data, this result makes the continuity of the solution map an optimal property. However, if a weaker Hr- topology is used then it is shown that the solution map becomes Hölder continuous in Hs.

Attributes

Attribute NameValues
URN
  • etd-03052013-151258

Author Melissa Davidson
Advisor Alex Himonas
Contributor Alex Himonas, Committee Chair
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2013-02-26

Submission Date 2013-03-05
Country
  • United States of America

Subject
  • soliton

  • wave equation

  • partial differential equation

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

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