Lets say we have a solution u, to the cauchy problem of the heat PDE:(adsbygoogle = window.adsbygoogle || []).push({});

u_t-laplacian(u) = 0

u(x, 0) = f(x)

u is a bounded solution, meaning:

u<=C*e^(a*|x|^2)

Where C and a are constant.

Then, does u is necesseraly the following solution:

u = integral of (K(x, y, t)*f(y))

Where K is the heat kernel?

Thanks in advance.

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# The heat kernel

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