# Is it possible to transform arithmetic-average strike continuous sampling Asian Black-Scholes equation to a heat equation?

By Transformation from the Black-Scholes differential equation to the diffusion equation - and back, we are able to transform vanilla European option into a heat equation.

And we know that the arithmetic-average strike continuous sampling Asian Black-Scholes equation is $$\frac{\partial V}{\partial t} +\frac{1}{2}\sigma^2S^2\frac{\partial ^2 V}{\partial S^2} +rS\frac{\partial V}{\partial S} + S\frac{\partial V}{\partial J}- rV=0$$ i.e., only one more term $$S\frac{\partial V}{\partial J}$$ compared with original BS equation.

Since this equation is similar to the original BS equation, I assume that we can transform it into a heat equation. Am I correct?