Advection diffusion equation The advection diffusion equation is the partial differential equation $$\frac{\partial C}{\partial t} = D\frac{\partial^2 C}{\partial x^2} - v \frac{\partial C}{\partial x}$$ with the boundary conditions $$\lim_{x \to \pm \infty} C(x,t)=0$$ and initial condition $$C(x,0)=f(x).$$ How can I transform the advection diffusion equation into a linear diffusion equation by introducing new variables $x^\ast=x-vt$ and $t^\ast=t$?
Thanks for any answer.

However, if the boundary conditions are for finite $x$, then for the transformed 
equation we have boundary conditions depending on time!! For example if $C$ denotes
a poluttant concentration, we see his value at some points.
