Can these panels be saved?

I'm not sure what happened to these rear seat panels, but they need help. In the first two photos, one of the panels is warped about 2" at one corner, and the vinyl is pulling back. The vinyl feels hard and would probably be crunchy and break off if I messed with it much.

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This photo is the other panel. It is warped a lot more, kind of like a potato chip, and has the same vinyl shrinkage issues going on.

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Can these panels be flattened out, and the vinyl conditioned somehow to make it pliable again? And if so, how does one go about stretching it or reattaching the vinyl to the panel backer?