My backpack 'fell' from a wall I placed it on a few months back and suffered a small crack in a corner on the base.
I tried to fix it by heating up a knife till it was red hot, and smoothing the plastic over. Unfortunately, the only effect it had was to turn the small crack into a hole!
After a trip to B and Q, I patched it up with some resin-putty stuff and it's been fine since.