- #1

fahraynk

- 186

- 6

The heat equation, change in concentration or temperature is equal to the average of its neighbors $$U_t=\alpha^2\nabla^2U$$

I was thinking its probably because the height of a point in the wave equation would need to keep going after it passes the average height of its neighbors, and then wobble back and forth. So even though it passes its neighbors it can still have a positive velocity and the acceleration will just flip signs.

But... why doesn't heat or concentration also do this? Why wouldn't the acceleration of change in temperature act more like a wave... or the velocity of a point on a drumhead just become 0 when its neighbors average is equal.

Do we not know, and the equations just model what we observe...or is there a reason?