The problem with white glue is the drying time, you may have to pin the pictures to the foam or it may peel away before the glue sets. Then there will be pinholes in the backdrop picture.
Contact cements or spray adhesive are often used, but their solvents may attack the foam as you mentioned in you post. DO NOT use these without trying them on a test piece of foam first.
The double sided tape referenced in pcarrell's post may be the best for your situation
George In Midcoast Maine, 'bout halfway up the Rockland branch
Hi guys,
I've got a problem I'm hoping someone can help out with. I'm building a new layout, and I need some advice on how to add a partial backdrop. I've already started to model a steel mill that is 11 feet in length (it is sitting on top of 3" pink foam). I'd like to add a partial backdrop to this area, but I don't know of the best way to do this. I'd like to use some of the scenery I've bought from scenic backdrop. Can I use regular white glue and post these backdrop scenery to 1"x2"s or will this not work. I've read in other forums that using glue on foam and backdrop scenery is not a good idea, as the backdrop can bubble up and get ruined. Any advice would be greatly appreciated. Thanks.