Fourier方法在偏微分方程理论中的应用

The Application of Fourier Method to the Theory of Partial Differential Equations

1882年,J.B.J.Fourier发表了他的著名论文《热分析理论》(Théorie Analytique dela chaleur).在此文中提出了一种十分巧妙的数学方法,即现在公认的Fourier方法.其直接目的是求解热传导方程,而今已发展成为一门独立的学科——Fourier分析,而且它的影响已深入到数学和自然科学的几乎每一个领域,发挥着极大的作用.

This paper presents a survey of three stages on the application of Fourier method to the theory of P.D.E..That is,Fourier method and its application to the theory of P.D.E. with constant coefficients; pseudodifferential operators and their application to the theory of general linear P. D, E., paradifferential operators and their application to the theory of non-linear P.D.E.