# The large-time structure of the solution to initial-value problems for a class of Burgers' equations with time dependent coefficients

Bait Ali Sulaiman, Faiza (2019). The large-time structure of the solution to initial-value problems for a class of Burgers' equations with time dependent coefficients. 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 initial-value problems based on a class of Burgers’ equations with time dependent coefficients. The normalized nonlinear paritial differential equation considered is given by

u$$_t$$ + t$$^δ$$uu$$_x$$ = u$$_x$$$$_x$$, −∞<x<∞, t>0.

where x and t represent dimensionless distance and time respectively, and δ (> −1) is a constant. In particular, we are interested in the emergence of coherent structures (com- posed of the expansion wave, Taylor shock wave profile, Rudenko-Soluyan wave profile, and the error function wave profile) 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
Smith, DavidUNSPECIFIEDUNSPECIFIED
Needham, David JohnUNSPECIFIEDUNSPECIFIED
Leach, John AndrewUNSPECIFIEDUNSPECIFIED
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Other
Other Funders: Ministry of Higher Education in Sultanate of Oman (MOHE)
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/9437

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