“heat equation”的概念、定义、翻译、参考文献-科学参考

heat equation

Mathematics

The heat equation states that the temperature T(x,t) in a uniform, solid medium satisfies the parabolic PDE

$\frac{\partial T}{\partial t} = κ \frac{\partial^{2} T}{\partial x^{2}},$

where κ‎ denotes the thermal diffusivity of the medium. In more than one spatial dimension the second derivative is replaced by the Laplacian ∇²T, and if κ‎ is not constant, then the RHS is replaced with div(κ‎∇T). The equation models diffusion more generally, for example that of particles, and so is often referred to as the diffusion equation.

单词	heat equation
释义	heat equation Mathematics The heat equation states that the temperature T(x,t) in a uniform, solid medium satisfies the parabolic PDE $\frac{\partial T}{\partial t} = κ \frac{\partial^{2} T}{\partial x^{2}},$ where κ‎ denotes the thermal diffusivity of the medium. In more than one spatial dimension the second derivative is replaced by the Laplacian ∇²T, and if κ‎ is not constant, then the RHS is replaced with div(κ‎∇T). The equation models diffusion more generally, for example that of particles, and so is often referred to as the diffusion equation.
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