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姓名 李育誠(Yu-cheng Lee)  查詢紙本館藏   畢業系所 數學系
論文名稱 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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摘要(中) 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.
摘要(英) 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.
關鍵字(中) ★ 雙曲守恆律
★ 非線性守恆律
★ 柯西問題
★ 整體經典解
★ 特徵線法
關鍵字(英) ★ Nonlinear balance laws
★ Hyperbolic conservation laws
★ Characteristic method
★ Global classical solutions
★ Cauchy problem
論文目次 中文摘要.................................................ⅰ
英文摘要.................................................ⅱ
1. Introduction...........................................2
2. Homogeneous System.....................................4
3. Non-homogeneous System................................10
4. Perturbed p-System with Source Term in Integral Form..13
5. A Uniform a-Priori Estimate...........................15
6. The Construction of h and Q...........................21
References...............................................23
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指導教授 洪盟凱(John M. Hong) 審核日期 2010-6-29
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