高维非线性波动方程整体解的渐近理论

The Asymptotic Theory of Global Solutions for Nonlinear Wave Equations in Higher-dimensions

本文采用整体迭代法,研究高维非线性波动方程Cauahy问题整体解的渐近理论,在Sobolev空间中,空间维数n>1+(2/a)(1+(1/a))时,证明了初值问题的适定性和形式近似解的合理性。

By the global iterative technique, this paper studies the asymptotic theory of global solutions of Cauchy' s problems for nonlinear wave equations in Higher - dimensions. In a suitable Sobolev space, with space dimension n>1+1/α(1+1/α), the wellposedness of the initial value problems and validity of formal approximations are demonstrated.