Global Classical Solutions for the 2 × 2 Nonlinear Balance Laws

• Main Authors: Yu-cheng Lee, 李育誠
• Other Authors: John M. Hong
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/74709341019960714764

碩士 === 國立中央大學 === 數學研究所 === 98 === 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.