The professionals doing repairs at a workplace seem to be capable of patching stairs with material so tough, and make it stick to the existing cement with such strength, that the patching survives years of use, even when it is done on the tip of a stair, as shown below.
My own needs are far more modest. Still, I'd like this not to be a job that looks bad after six months, and that gets completely detached after twelve. My garage floor is abraded in a few places. No place is worse than the one letting air through under the garage door.
I know that I could use some cement, but that will not last very long. Can you guess what material has been used on the stairs above, or can you suggest some material that will provide a semi-permanent solution? I am quite happy using an entirely different color (I'll paint with an epoxy-based paint at some point anyway), just so long as it lasts.