二階非線性守恆律的整體經典解; Global Classical Solutions for the 2 × 2 Nonlinear Balance Laws

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题名:	二階非線性守恆律的整體經典解;Global Classical Solutions for the 2 × 2 Nonlinear Balance Laws
作者:	李育誠;Yu-cheng Lee
贡献者:	數學研究所
关键词:	雙曲守恆律;非線性守恆律;柯西問題;整體經典解;特徵線法;Nonlinear balance laws;Hyperbolic conservation laws;Characteristic method;Global classical solutions;Cauchy problem
日期:	2010-06-29
上传时间:	2010-12-08 14:26:13 (UTC+8)
出版者:	國立中央大學
摘要:	在這篇論文中,我們討論二階非線性系統守恆律的整體經典解存在性.使用特徵線法和A uniform a priori estimate我們去建立整體經典解的存在條件. In this thesis, we consider the Cauchy problem of 2 × 2 nonlinear hyperbolic balance laws whose source terms consist of the integral of unknowns. Such nonlinear balance laws arise in, for instance, the compressible Euler-Poisson equations of gas dynamics in Lagrangian coordinate. We are concerned with the global existence of classical solutions to the Cauchy problem of such differential-integro systems. We extend the results by Ta-tsien Li for quasilinear hyperbolic systems to our nonlinear balance laws. The method in this thesis based on the following three steps: (1) the theory of local classical solutions, (2) uniform a priori estimate, (3) global existence or blow up of classical solutions. We find the transformation so that the 2 × 2 system for the first derivatives of Riemann invariants are de-coupled under this transformation. So, the characteristic method for scalar equations can be applied.
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