For an odd application of PDE: you can define and solve boundary value problems over spatial domains in games to find a solution over the playing field that measures how near or far you are from desireable or undesireable locations. Then objects in the game (e.g. actors controlled by AI) can use simple gradient ascent / gradient descent using the local gradient of the solution to determine how to move, in order to e.g. avoid threats or chase the player

https://sgd.cs.colorado.edu/wiki/Collaborative_Diffusion