My cat had this a while ago. It went away fairly quickly after I changed his dish from a ceramic one to stainless steel, and removed their plastic mats and put down little placemats instead.
I recommend stainless steel (ceramic over time can get the little hairline cracks and bacteria can get in). Also clean the dish between feedings, i.e., never put fresh food in a dirty dish.
The plastic placemat advice above is also good.
Also, if you use hydrogen peroxide, please dilute it before using it. Hydrogen peroxide burns even healthy tissue so dilution helps stop that.
My show cat Veeshan gets really bad acne. I was using peroxide and it was not helping. Well another breeder mentioned to me that just warm water and a wash cloth should do the trick. And it works! Gently scrub off the black stuff with warm water and a wash cloth once a day.
Huh, warm water, eh? I'm going to try that. I'm thinking he has some kind of allergy. I switched from plastic to stainless awhile ago and the acne never went away. I'll try the warm water. Is this something that certain cats will just get, forever? Thanks for the tips.