热传导方程中傅氏积分与傅氏变换的应用

Application of Fourier Integral and Fourier Transform in Heat Conduction Equation

热传导方程是最简单、最典型的抛物型方程。许多热传导中的主要定解问题,例如柯西问题及混合问题,都需要运用傅里叶积分与傅里叶变换。傅里叶积分变换有许多的性质都是值得学习运用的,尤其是傅里叶变换在不同的领域有不同的形式,比如现代声学、声呐、地震、核科学乃至生物医学等方面广泛的应用。

The heat conduction equation is the simplest and most typical parabolic equation.Many of the main fixed-solution problems in heat conduction,such as Cauchy problem and mixed problem,need to use Fourier integral and Fourier transform.Fourier integral transform has many properties.It is worth learning and using,especially the Fourier transform has different forms in different fields,such as modern acoustics,sonar,earthquake,nuclear science,and even biomedical applications.