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

[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 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\(_x\)\(_x\), −∞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.

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

[关键词] Q Science;QA Mathematics