Can S2 Solve the Diffusion Equation in 2D?

[theneedtoknow]

Show that S2 = S(x,t)S(y,t) solves St = k (Sxx + Syy)

well
St = St(x,t)S(y,t) + S(x,t)St(y,t)
Sxx = Sxx(x,t)S(y,t)
Syy=Syy(y,t)S(x,t)

but what do i do from there?

 

[fzero]

Presumably S(x,t) is the solution to a closely related equation?

 

[theneedtoknow]

Well yeah, I thought about assuming that S(x,t) and S(y,t) solve the 1d diffusion equation in their respective dimensions, and then it's easy to just replace all the Sts with the Sxx and Syys, but the question doesn't provide any assumptions about S(x,t) and S(y,t) being solutions to the 1d equation. Is that just something I should assume anyway?

 

[fzero]

If you divide through by S(x,t)S(y,t) you will be able to find the equation that S(x,t) must satisfy. It's not quite the 1d diffusion equation, but it looks easy to solve.