Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/21289| Title: | Well-Posedness of a Nonlinear Wave Equations in Characteristic Coordinates |
| Authors: | Sakovich, Anton |
| Advisor: | Pelinovsky, Dmitry |
| Department: | Mathematics |
| Publication Date: | Jan-2009 |
| Abstract: | We prove global well-posedness of the short-pulse equation with small initial data in Sobolev space H^2. Our analysis relies on local well-posedness results of Schafer and Wayne, the correspondence of the short-pulse equation to the sine-Gordon equation in characteristic coordinates, and conserved quantities of the short-pulse equation. We perform numerical computations to illustrate this result. We also prove local and global well-posedness of the sine-Gordon equation in an appropriate vector space. |
| Description: | Title: Well-Posedness of a Nonlinear Wave Equations in Characteristic Coordinates, Author: Anton Sakovich, Location: Thode |
| URI: | http://hdl.handle.net/11375/21289 |
| Appears in Collections: | Digitized Open Access Dissertations and Theses |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Sakovich_Anton_2009_01_master.pdf | Title: Well-Posedness of a Nonlinear Wave Equations in Characteristic Coordinates, Author: Anton Sakovich, Location: Thode | 15.54 MB | Adobe PDF | View/Open |
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