If it says requires concentration, then it seems to persist until something breaks concentration in the same ways it breaks in normal 5e rules; I.E. casting another concentration spell, resting, dying, or failing a check when you take damage.
The difference from tabletop, is they don't seem to have a time limit other than the time between rests if you don't break it another way. I'm not sure if this is intention to make the gameplay less tedious with micromanaging rounds outside of combat, or if they just haven't gotten the timers working yet. I hope for the most part that it's the former, because I think most spells lasting one minute or less is one of the worst changes from earlier editions. In 2e you were invisible 24 hours for example, which was nice, and 5e's concentration created a way to balance it nicely without even needing time limits at all.
The side-effect stuff like cantrips lighting people on fire is more ambiguous how long it will last until you look at the debuffs. And the abundant surface elemental damage seem to be holdovers from DOS games, since the load screen tips imply there should be less of it than in their previous games.