I have a function f(S,t), which satisfies some PDE, with the condition that f(S,T) = max\{S-1,0\}. I introduce two new variables x and \tau as follows:

S = e^x and t=T-\frac{2\tau}_{\sigma^2}, and define the function W by f(S,t) = W(x,\tau). Is the new initial condition going to be:

f(S,T)=W(x,\tau(t)=T)=W(x,0)=\{e^{x}-1,0\}?

Thanks.