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):