Hi

I have the heat equation

$\displaystyle \frac{\partial u}{\partial \tau}=\frac{\partial^2 u}{\partial x^2}$

where -infinity< x <infinity

and tau>0

with u(x,0)=H(x) the heavyside function

and I'm looking for a solution of the form u(x, tau)=U(y) where y=x/sqrt of tau.

How do the boundary conditions become

U(-infinity)=0

and

U(infinity)=0

I did something and got 1/0!! maybe limits are needed? Thanks for any help