积分变换在数理方程中的应用

The Application of the Integral Transform in the Equations of Mathematical Physics

积分变换是研究数理方程的重要工具.利用Fourier变换或Laplace变换,可以求得一些数理方程的显式解.事实上,对于一些半无界问题的数理方程如热传导方程,可以进行Fourier-Laplace变换,通过寻求半无界问题的Green函数和全空间问题热核的关系,给出半无界问题解的表达式.

Integral transform is an important tool to study the equations of mathematical physics.The Fourier transform or Laplace transform can be used to solve some equations of mathematical physics and get the explicit solutions.In fact,for some half-space problem of the equations of mathematical physics,e.g.,heat equation,one can use the Fourier-Laplace transform to find the relationship between the Green function of the half-space problem and the heat kernel of the full space problem,and get the solution for the half-space problem.