FWIW Raka epoxy is 1/2 to 2/3rds the cost of West Systems and by my experience and that of others, it's just as good. A bonus is the straight 2:1 mix of resin to hardener, so no expen$ive pumps are needed. I've mixed from 2-to-1 capfulls to 8-ounce yogurt containers ... and it works slick! See
www.raka.com and call or email Larry @ Raka if you need specific guidance. He's awesome to deal with!
That said, my door is worse than yours. I did what others suggested, I warmed the door with a slightly damp cloth and used a clothes iron to iron flat the pieces. Then I injected epoxy into the cracks, covered the bad area with wax paper sprayed with Pam cooking spray with olive oil (as a release agent) and left some 'heavy' items on it to cure so the delam would lay flat. CAUTION: You need to have the door OFF and make sure you have the entire OPPOSITE site of the door supported, NOT the frame. Otherwise you will get a bulge.
This will work and last you a few seasons, but once water gets int ehre ... it's only a matter of time 'til you will eventually replace it. I'd say, looking at yours, if you do as I suggest (there may be other methoids) you might even fix it but good, as mine was much worse than yours when I effected my repair and I still got 3 season out of it, maybe 4. Make sure to seal the OTHER side too, as moisture is insidious and will get in however and wherever it can.