Citation
Ellison, James Auby (1971) Existence, Uniqueness, and Stability of Solutions of a Class of Nonlinear Partial Differential Equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VBKZ-1R69. https://resolver.caltech.edu/CaltechTHESIS:03292013-085108737
Abstract
In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Subject Keywords: | (Applied Mathematics and Philosophy) |
| Degree Grantor: | California Institute of Technology |
| Division: | Engineering and Applied Science |
| Major Option: | Applied Mathematics |
| Minor Option: | Philosophy |
| Thesis Availability: | Public (worldwide access) |
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| Thesis Committee: |
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| Defense Date: | 24 August 1970 |
| Record Number: | CaltechTHESIS:03292013-085108737 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:03292013-085108737 |
| DOI: | 10.7907/VBKZ-1R69 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 7561 |
| Collection: | CaltechTHESIS |
| Deposited By: | Benjamin Perez |
| Deposited On: | 29 Mar 2013 16:11 |
| Last Modified: | 20 Jun 2024 22:09 |
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