I have a heat equation given as:
$\partial_{t}v + \frac{\sigma^{2}}{2s^{2}}\partial_{yy}v - \frac{\sigma^{2}}{2} = 0$
where $s$ is a variable and $v = v(t,y)$. Now, in the article I'm reading, it is implied that this equation can be transformed into the equation:
$\partial_{t}w + \frac{\sigma^{2}}{2}\partial_{xx}w + \frac{\sigma^{2}}{2}\partial_{x}w = 0$
where $w = w(t,x)$
I'm attempting to follow a similar method as to transforming the Black-Scholes equation into the heat equation, as given in the link: http://planetmath.org/AnalyticSolutionOfBlackScholesPDE
However, all attempts I've made have failed. Can someone provide a bit of a hint as to what should be done? Is it even possible to transform this equation?