 Wave equation

Describes perfect lossless waves on the surface of a string, or on a water surface.

Uniqueness: math.stackexchange.com/questions/1113622/uniqueness-of-solutions-to-the-wave-equation

As mentioned at: math.stackexchange.com/questions/579453/real-world-application-of-fourier-series/3729366#3729366 from solving partial differential equations with the Fourier series citing courses.maths.ox.ac.uk/node/view_material/1720, analogously to the heat equation, the wave linear equation can be be solved nicely with separation of variables.