Dafermos Regularization of a Modified KdV-Burgers Equation
| dc.contributor.advisor | Dr. Xiao-Biao Lin, Committee Member | en_US |
| dc.contributor.advisor | Dr. Pierre Gremaud, Committee Member | en_US |
| dc.contributor.advisor | Dr. Michael Shearer, Committee Member | en_US |
| dc.contributor.advisor | Dr. Stephen Schecter, Committee Chair | en_US |
| dc.contributor.author | Taylor, Monique Richardson | en_US |
| dc.date.accessioned | 2010-04-02T18:43:07Z | |
| dc.date.available | 2010-04-02T18:43:07Z | |
| dc.date.issued | 2010-03-19 | en_US |
| dc.degree.discipline | Applied Mathematics | en_US |
| dc.degree.level | dissertation | en_US |
| dc.degree.name | PhD | en_US |
| dc.description | North Carolina State University Theses Mathematics.;North Carolina State University Theses Mathematics. | |
| dc.description.abstract | This project involves Dafermos regularization of a partial differential equation of order higher than 2. The modified Korteweg de Vries-Burgers equation is u_T + f(u)_X = alpha u_XX +beta u_XXX, where the flux is f(u) = u^3, alpha> 0, and beta is nonzero. We show the existence of Riemann-Dafermos solutions near a given Riemann solution composed of shock waves using geometric singular perturbation theory. When beta > 0, there is a possibility that the Riemann solution is composed of two shock waves as opposed to one. In addition, we use linearization to study the stability of the Riemann-Dafermos solutions. | en_US |
| dc.format | Thesis (Ph.D.)--North Carolina State University. | |
| dc.identifier.other | etd-01082010-100837 | en_US |
| dc.identifier.uri | http://www.lib.ncsu.edu/resolver/1840.16/4034 | |
| dc.rights | I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. | en_US |
| dc.subject | Geometric singular perturbation theory | en_US |
| dc.subject | Partial differential equations | en_US |
| dc.title | Dafermos Regularization of a Modified KdV-Burgers Equation | en_US |
| dcterms.abstract | Keywords: geometric singular perturbation theory, partial differential equations. | |
| dcterms.extent | ix, 75 pages : illustrations (some color) |
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