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Student Number 952201025 Author Man-meng Io(姚文銘) Author's Email Address ar_gold@yahoo.com Statistics This thesis had been viewed 1212 times. Download 534 times. Department Mathematics Year 2007 Semester 2 Degree Master Type of Document Master's Thesis Language English Title Classical Solutions to the Perturbed Riemann Problem of Scalar Resonant Balance Law Date of Defense 2008-06-14 Page Count 24 Keyword Characteristic method Conservation laws Lax's method Nonlinear balance laws Perturbed Riemann problems Riemann problems Abstract In this paper we study the classical solutions to the perturbed Riemann problem of some scalar nonlinear balance law in resonant case. The equation with source term is equivalent to a 2×2 nonlinear balance laws as described in [6, 7], and it is a resonant system due to the fact that the speeds of waves in the solution to this 2×2 system coincide. The characteristic method in [8] is applied to construct the classical solutions of perturbed Riemann problem. Moreover, we show that, the pointwise limit of classical solutions, which are deﬁned as the

measurable solutions to the corresponding Riemann problem (with singular source) of perturbed Riemann problem, are self-similar as described in [12].Table of Content 中文摘要 ………………………………………………………………i

英文摘要 ………………………………………………………………ii

Acknowledgement ………………………………………………………iii

目錄 ……………………………………………………………………iv

圖目錄 …………………………………………………………………v

表目錄 ……………………………………………………………………vi

1. Introduction …………………………………………………………2

2. Classical solutions of perturbed Riemann problem …………5

3. Stability of perturbed Riemann solutions …………………17

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