The large-time solution of nonlinear evolution equations

[摘要] 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.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics