A self-inflating tire assembly includes an air tube mounted within a tire sidewall or chafer groove. The air tube is in contacting engagement with opposite angled groove surfaces surrounding the air tube. A segment of the air tube is flattened from an expanded diameter to a flat diameter by bending and compression of the groove in a rolling tire footprint to force air evacuated from the flattened segment along a tube air passageway. A coverstrip overlays and seals the groove and provides an abrasion resistant surface on the exterior of the tire. The coverstrip is made from a vulcanizable rubber composition comprising from 50 to 80 phr of a polybutadiene, from 50 to 20 phr of natural rubber, and from 0.1 to 5 phr of a vulcanization modifier.