- #1
yetar
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Lets say we have a solution u, to the cauchy problem of the heat PDE:
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.
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.