you can use superglue, any superglue on polystyrene, polystyrene is the sheet plastic (for some reason known as styrene sheet by a lot of modellers), obviously you can use MEK weld or polyweld plastic cements as well
On EPS (polystyrene foam, expanded polystyrene, white foam( and most other foams)) you can use odourless cyanoacrylate (foam freindly superglue) (not the standard types), foam safe contact glues such as our Depbond (solvent based) or Depbond Pro.W (solvent free), PVA and Aliphatic resins are slow to dry but can be used on small areas , epoxy resins can be used with no problems as they have no solvents (never use polyester resin) , Most foaming polyurethane glues such as Xbond can be used as well