半线性Klein—Gordon方程Cauchy问题整体解存在定理GLOBAL EXISTENCE THEOREM OF SOLUTION FOR CAUCHY PROBLEM FOR SEMILINEAR KLEIN-GORDON EQUATION
盛其荣;
摘要(Abstract):
本文讨论半线性Klein—Gordon方程Cauchy问题。对初值φ(x)、ψ(x),对空间维数n及半线性项加以适当限制,在Sobolev空间框架下、用不动点原理得到了整体解的存在唯一性。
关键词(KeyWords): 半线性;小初值;不动点;能量估计
基金项目(Foundation):
作者(Authors): 盛其荣;
参考文献(References):
- 1 S.Mizohota, The Theory of Partial Differential Equations. 1973, Cambridge Univ Press.
- 2 F.John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28, (1979) , 235-265.
- 3 Hayashi, N. Tsutsumi, M.:Non-relativistic approximation of non-linear klein-Gordon equation, preprint.
- 4 Marshall, B.:Mixied norm estimates for the Klein-Gordon equation(1981) preprint.
- 5 李大潜、陈韵梅,非线性发展方程(讲义)(1986) .
- 6 Shatah, J. L, Globol existence of small to non-linear evolution equation, preprint.
- 7 复旦大学,数学物理方程(第二版),科技出版社,(1978) .
- 8 S.Klainerman & Gustaro Ponce, Global Amplitude solution to nonlinear evolution equation. CPAM, Vol.XXXVl(1981) .