本文利用物理学中常见的热传导理论，形象地阐释了二阶齐次线性偏微分方程的本质。
With the ordinary theory of Heat Exchange in physics this essay visualizes the essence of second-order homogenous linear partial differential equations.
抛物型积分微分方程多出现在记忆材料的热传导、多孔粘弹性介质的压缩、原子反应、动力学等问题中。
The integro-differential equation of parabolic type often occurs in applications such as heat conduction in materials with memory, compression of viscoelastic media, nuclear reactor, dynamics, etc.
首先，根据热传导的基本原理，建立温度场的傅立叶导热微分方程。
Firstly, in the sight of basic principle on conductions of heat, Fourier heat conduction differential equation of temperature field is founded.
又对于变密度、变比热、变导热系数这样的更一般的情况也推立了六个二阶热传导的微分方程。
By the way, for the case of variable density, specific heat as well as thermal conductivity, we have been successful to deduce other similar six heat transfer differential equations.
合并不同阶的均匀化非傅立叶热传导方程，消去缩小时间尺度参数，得到四阶微分方程。
By combining various orders of homogenized non-Fourier heat conduction equations, the reduced time dependence is eliminated and the fourth-order differential equations are derived.
当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。
The nonlinear equation of heat conduction is transformed into a Laplace's equation by applying the Kirchhoff transformation, and an analytic approximate solution of the equation is derived.
这是傅立叶热传导定律，这是一个偏微分方程序，我们拥有世上唯一写上偏微分方程序的食谱。
This is Fourier's law of heat conduction. It's a partial differential equation. We have the only cookbook in the world that has partial differential equations in it.
这是傅立叶热传导定律，这是一个偏微分方程序，我们拥有世上唯一写上偏微分方程序的食谱。
This is Fourier's law of heat conduction. It's a partial differential equation. We have the only cookbook in the world that has partial differential equations in it.
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