In the inhomogeneous heat equation
ut(t; x) =
u(t; x) + f(t; x);
The term f models the interruptions to the heat diusion along time and on space locations.
Especially, the eect of f in time direction is more troublesome and the regularity of u is subject
to the regularity of f. In this talk we discuss a type of modeling of f in the form Nt(!)g(t; x),
where N is a random noise process which can be whiter than the white noise. We also discuss
a regularity relation between Ng and u.