非线性波动系统的冲击层解

Shock Layer Solution of Nonlinear Wave System

考虑非线性奇异摄动波动方程第三边值问题,先利用奇异摄动法构造外部解,再引入伸长变量依次得到解的冲击波尖层、初始层及边界层的校正项,最后给出问题解的渐近展开式,并证明渐近解的一致有效性.

We considered the third boundary value problem of nonlinear singularly perturbed wave equation. Firstly, the outer solution was constructed by using singular perturbation method. Secondly, correction terms of the shock layer, initial layer and boundary layer were obtained by using the stretched variables. Finally, the asymptotic expansion of solution to problem was given , and the uniform validity of its asymptotic solution was proved.