Originally posted by: CycloWizard
Originally posted by: Cerpin Taxt
You apparently do not understand what predictions are. Predictions say "X is true iff Y." Your #2 says "X is true, despite Y."
I'm not sure if you're thick headed, illiterate, or just really having a hard time reading my broken English here. I'll give a more concise mathematical example again, and if you still can't get it, I'll give up.
If I have some quantity u (could be temperature, mass fraction, or velocity, whichever you like), then the 1-D transient diffusion equation is simply
du/dt=d^2u/dx^2,
where t is time and x is the spatial coordinate. If I supply boundary conditions u(x=0)=1 and u(x=1)=0 and the initial condition u(t=0)=u_0, I can solve the governing equation and get some infinite series solution very easily (though it's nasty to type out or read in plain text ). The steady state solution is simply
u(x)=1-x.
This is exactly equivalent to hypothesis #1 if I set u_0=0. This is exactly equivalent to #2 if I set u_0=any solution of the general case with u_0=0. Most obviously, they are identical if I let u_0=1-x, in which case the solution for case #2 is simply the steady state case. So, for any arbitrary initial condition u_0, the predicted profile for u(x) is absolutely identical at all times as long as the selected u_0 is a solution to the problem with u_0=0.