三维空间中半线性波方程整体解的渐近性

The Asymptotic Property of Global Solutions for Semilinear Wave Equations in Three Space Dimensions

研究三维空间中半线性波方程utt-△u=εf(u ,ε) , t >0 ,u(0 ,x ,ε) =u0 (x ,ε) ,ut(0 ,x ,ε) =u1 (x ,ε) ,(其中 x∈R3 ,u是一个实值未知函数 ,△ =∑3i =1 2 x2 i,ε充分小且 0 <｜ε｜≤ε0 1,)整体解的渐近性 ,得到了在C2 空间中时间T =∞时形式近似解的合理性及适定性 .

This paper deals with the asymptotic theory of initial value problems for semilinear wave equations in three space dimensions. The well posedness and validity of formal approximations about time T =∞ are discussed in the classical sense of C 2. These results describe the validity of formal global solutions.