On a Long Range Scattering for the nonlinear Klein-Gordon equation

• Main Authors: Jheng-HongLiou, 柳政宏
• Other Authors: Yung-fu Fang
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/g4qpm9

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 101 === This paper is based on 'A Remark on Long Range Scattering for the Nonlinear Klein-Gordon Equation',which is published by Hans Lindblad and Avy Soffer in 2008, and we make some additional proofs and interpretations. First, in order to observe the form of the solution, we discuss the asymptotic solution of the linear equations. When we find the general solution,we observe the form of firsr-order asymptotic solution of ODE,thus we observe the form of firsr-order asymptotic solution of PDE. Finally,we can use the previous parts to observe the form of higherorder asymptotic solution of PDE.In addition, we illustrate the procedure of solving related of ODE and PDE. We interpret their thinkings and concepts clearly in detail. We hope this thesis can help readers to understand the meaning of the paper sufficiently and easily. Key words: Nonlinear Klein-Gordon Equation; Scattering Theory.