The solution for a point source for the heat equation given above is an example of the use of a Fourier integral.
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The heat equation is, technically, in violation of special relativity, because its solutions involve instantaneous propagation of a disturbance.
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Given a block of ice, one can solve the heat equation given appropriate initial and boundary conditions to determine its temperature.
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The Weierstrass transform is intimately related to the heat equation ( or, equivalently, the diffusion equation with constant diffusion coefficient ).
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Examples include approaches to solving the heat equation, Schr�dinger equation, wave equation, and other partial differential equations including a time evolution.
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"Transient conduction " ( see Heat equation ) occurs when the temperature within an object changes as a function of time.
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An important practical example is Fourier's law ( heat flux is proportional to temperature gradient ) to arrive at the heat equation.
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Burgers'equation can notably be converted to a heat equation through a nonlinear substitution, as suggested by E . Hopf in 1950.
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This is known in other fields as the diffusion equation or heat equation, it is a parabolic partial differential equation ( PDE ).
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:There is a specialised description, the heat equation, but it is probably more complex than what you're looking for.
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