n维非线性波动方程组解的渐近理论

An Asymptotic Theory of Solutions for Systems of n-Dimensional Nonlinear Wave Equations

研究n维非线性波动方程组Cauchy问题的渐近理论 ,通过利用对应线性齐次波动方程组的解的估计 ,在时间变量 0 t O(|ε|-1)的Sobolev空间中 ,证明了初值问题的适定性和形式近似解的合理性 .

This paper studied the asymptotic theory for Cauchy's problems for systems of n dimensional wave equations, by estimating the solution for systems of corresponding homogeneous linear wave equations. In a suitable Sobolev space on the time scale of O(|ε| -1 ) , the wellposedness of the initial value problems and validity of formal approximations are demonstrated.