We would recommend using our Liquid Nails Landscape or Selleys 650fc Adhesive/Sealant.
If the rubber is going to be in a high-traffic area, or will have vehicles driving over the strip, you may need to consider securing the strip to the concrete with mechanical fasteners as well.
Liquid Nails Landscape and Selleys 650FC Adhesive/Sealant are highly water resistant and weatherproof.