Hanaç, Esen (2015). The large-time solution of nonlinear evolution equations. University of Birmingham. Ph.D.
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Hanac15PhD.pdf
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Abstract
In this thesis we use the method of matched asymptotic coordinate expansions to examine in detail the structure of the large-time solution of a range of initial-value and initial-boundary value problems based on Burgers' equation or the related Burgers-Fisher equation. The normalized nonlinear partial differential equations considered are:
(i) Burgers' equation
Ut + UUx - Uxx = 0.
(ii) Burgers-Fisher equation
Ut + kuux = Uxx + u( 1 - u).
Here x and t represent dimensionless distance and time, respectively, while k (≠ 0) is a constant. In particular, we are interested in the emergence of coherent structures (for example: expansion waves, stationary states and travelling waves) in the large-time solution of the problems considered.
| Type of Work: | Thesis (Doctorates > Ph.D.) | |||||||||
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| Award Type: | Doctorates > Ph.D. | |||||||||
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| College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | |||||||||
| School or Department: | School of Mathematics | |||||||||
| Funders: | None/not applicable | |||||||||
| Subjects: | Q Science > QA Mathematics | |||||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/6091 |
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