HDPE will respond to heat, if you can get some water very hot, and stabilize the shape of the walls, fill it past the damaged part. If it is torn, you will have to weld it. No solvents will glue it.
HDPE can be repaired by bonding, as long as you use a product that is also HDPE-based. Araldite® epoxy-based resins do not hold. But in your case, given that the tank is deformed as a result of suction, it might be better to replace it with a reinforced tank that can resist the force when vacuumed.
The link below is a French supplier: