A very simple solution to the diffusion equation is $u(x,t)=x^2+2 t$
My question:
How can this be a solution to the diffusion equation when nothing really diffuses, but just stays the same - see plot: Here
I can see that it is a solution but can't believe my eyes... Is there some kind of intuition other than: "it satisfies the PDE"?
Are there other examples of solutions to well-known equations that behave completely un-intuitive in some situations?