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Get some border adhesive, usually available in a small tube. Take a filler knife or scraper blade and gently run it under the paper to lift the edge slightly. Using a syringe or if you are lucky the pointed nozzle on your border adhesive squeeze a load of adhesive under the paper. Rub the paper lightly with a sponge and thoroughly clean all the adhesive that comes out of the crack. The better you clean off the glue the better your paint will look. Leave it to dry and you should have solved your problem.
You can bodge it with super glue if you are in a desperate hurry. Not recommended for a lot of reasons. I have a lovely little tool called a seam roller, not only does it help to do this job but it helps to make sure it never happens in the first place!
I'm painting over lining paper (dark green).
Some of the sections over the rad have curled up / separated.
What's the best way to make them flat?
Cheers.
Pic2 = very close up
Pics1&3 = more accurate representation irl