The large-time solution of nonlinear evolution equations

Hanaç, Esen (2015). The large-time solution of nonlinear evolution equations. University of Birmingham. Ph.D.

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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.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Leach, John AndrewUNSPECIFIEDUNSPECIFIED
Needham, David JohnUNSPECIFIEDUNSPECIFIED
Licence:
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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