Equilibrium Temperature Distributions - Partial Differential Equations | Lecture 3

Much like in dynamical systems, equilibria (or fixed points or steady-states) play a critical role in understanding the behaviour of partial differential equations. In this lecture we introduce the concept of an equilibrium to a partial differential equation with the heat equation. We will see that this results in an ordinary differential equation for an equilibrium that is a function over just the spatial variable. Furthermore, we evoke our intuition of the physical process of heat flow to understand the long-time behaviour of time-dependent solutions to the heat equation without solving it explicitly... yet.

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[zrmsraggot]

I can wrap my mind around the fact heat will average around a temp but can't seem to do so with water level in the pool 😅