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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The heat kernel

**Physics Forums | Science Articles, Homework Help, Discussion**