Citation
Hagan, Patrick Shawn (1979) The Stability of Traveling Wave Solutions of Parabolic Equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yn9e-nm19. https://resolver.caltech.edu/CaltechTHESIS:03222013-083627751
Abstract
A method for determining by inspection the stability or instability of any solution u(t,x) = ɸ(x-ct) of any smooth equation of the form u_t = f(u_(xx),u_x,u where ∂/∂a f(a,b,c) > 0 for all arguments a,b,c, is developed. The connection between the mean wavespeed of solutions u(t,x) and their initial conditions u(0,x) is also explored. The mean wavespeed results and some of the stability results are then extended to include equations which contain integrals and also to include some special systems of equations. The results are applied to several physical examples.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Subject Keywords: | (Applied Mathematics) |
| Degree Grantor: | California Institute of Technology |
| Division: | Engineering and Applied Science |
| Major Option: | Applied Mathematics |
| Thesis Availability: | Public (worldwide access) |
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| Thesis Committee: |
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| Defense Date: | 1 April 1979 |
| Record Number: | CaltechTHESIS:03222013-083627751 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:03222013-083627751 |
| DOI: | 10.7907/yn9e-nm19 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 7549 |
| Collection: | CaltechTHESIS |
| Deposited By: | Benjamin Perez |
| Deposited On: | 25 Mar 2013 15:52 |
| Last Modified: | 27 Nov 2024 20:22 |
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