Difficulties warping a comp to fit a curved screen image.

Hey, 

I'm having this issue that might be easy to solve, but I just can't seem to do it.

I need to do a mock-up of the bottom comp on the curved screen image on top. It's a static image so it won't require and tracking, but I just don't know how to do it - I've tried a lot of distort tools and combinations of them, without much success.

Any ideas?

thank you!