How to stop/fade wave propagation in dynamic paint?

currently I’m using a mesh as an particle emitter and brush to bombard a dynamic paint canvas to create waves going all directions. My goal is to fade/stop the propagation towards the rim of the canvas, but somehow my knowledge with Weight Paint seems to fail me at that point.

Has anyone a clue?

Thanks in advance

You could have the dynamic paint creating an image sequence, and run that image sequence through a displacement modifier… and then use a vertex group to fade out the displacement modifier around the edge of the object.