具有常重特征的擬線性雙曲方程非線性初邊值問題的適定性.pdf

1、上海交通大學(xué)碩士學(xué)位論文具有常重特征的擬線性雙曲方程非線性初邊值問題的適定性姓名：陳瑋申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王亞光20081201上海交通大學(xué)碩士學(xué)位論文 Abstract Well-posedness of Nonlinear Initial Boundary Value Problems

2、 of Quasilinear Hyperbolic Equations with Constant Multiple Characteristics ABSTRACT Many physics phenomena can be described by quasilinear hyperbolic equations. Mathematical theories on the initial boundary value probl

3、ems have many important applications in gas dynamics, plasma physics, acoustics, hydrodynamics, and so on. In recent years, there already have been many qualitative researches on quasilinear hyperbolic equations, which m

4、ainly focus on the existence, regularity and decay estimates of local and global solutions. Most researchers are only dealing with linear boundary conditions. However, with the development of applications and theoretical

5、 researches, it is important and challenging to study the problems with a nonlinear boundary condition. In this thesis we mainly study initial boundary value problems for quasilinear hyperbolic equations with nonlinear b

6、oundary conditions. By assuming that the equations have constant multiple characteristics and the corresponding linearized problems satisfy the uniform Lopatinski condition, we get the well-posedness of the initial bound

7、ary value problem with nonlinear boundary conditions. The main processes are as follows. First, we establish a series of the energy estimates for the solutions to the linearized problems. Next, we construct approximation

8、 solutions of the nonlinear problems by using the Picard iteration for the equations and the Newton iteration for the boundary conditions. Then, we get the boundness and convergence of the approximation solutions by usin