Sika make a range of sealant products and one of them will be for perspex. Don't use Sika 291 as it will let go from perspex over time. Good for most other substrates though. 3M also do some similar sealants and then there are quite a few others as well. The big thing is to make sure that it will adhere to the perspex as quite a few will let go over time. Read the instructions. Check 3M 5200 as one idea. It seems to permanently stick most things.