一类非线性发展方程及其应用

A Class of Nonlinear Evolution Equations and Its Applications

本文讨论了如何由齐线性方程（组）初值问题解的衰减估计来构造其相应半线性问题“小初值”整体解及其渐近性，并将其结果应用于半线性热传导方程、Ｓｃｈｒｄｉｎｇｅｒ方程（组）等Ｃａｕｃｈｙ问题，得到一系列有关结果．

In this paper, how to construct the global solution with 'small initial data' and its asymptotic property of the semilinear problem according to the decaying estimates of the solution to its corresponding homogeneous problem is discussed its results can be applied to semilinear heat equations, Schrodinger equations or systems and a series of results are obtained about them.