Aspects of the mathematical theory of water waves
Citation:
David Henry, 'Aspects of the mathematical theory of water waves', [thesis], Trinity College (Dublin, Ireland). School of Mathematics, 2007, pp 95Download Item:
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Abstract:
In this thesis we study various aspects of the mathematical theory of water waves.
In Chapter 2 some qualitative results for two recently-derived nonlinear models for shallow
water waves are presented. In the first part of the chapter we examine the solutions
of a family of nonlinear differential equations which initially have compact support, and
investigate whether they retain this property over a nontrivial time interval. In the second
section of Chapter 2 we particularise to the Degasperis-Procesi equation and conduct a
more detailed analysis of the propagation speed of solutions for a larger class of initial data,
achieving results on the persistence properties of solutions and the unique continuation of
solutions.
Author: Henry, David
Advisor:
Constantin, AdrianQualification name:
Doctor of Philosophy (Ph.D.)Publisher:
Trinity College (Dublin, Ireland). School of MathematicsNote:
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Mathematics, Ph.D., Ph.D. Trinity College DublinLicences: