Simon Cowell Is 'Healing Well' as Heidi Klum, Sofia Vergara and Howie Mandel Judge AGT: Source

Heidi Klum, Sofia Vergara and Howie Mandel were without a guest judge on Tuesday night's episode

America's Got Talent continues onto its third week of live quarterfinals — as series creator Simon Cowell enters his third week of recovery.

Seventeen days since Cowell, 60, has been out due to injury, judges Heidi Klum, Sofia Vergara and Howie Mandel were without a guest judge on Tuesday night as the trio and host Terry Crews kicked off the third round of live shows to watch 33 out of 44 acts compete for a spot in the semifinals.

This week's contestants included aerial act Alan Silva, singer Annie Jones, contortionist dance group Bone-Breakers, singer and Klum's Golden Buzzer recipient Cristina Rae, dance group Dance Town Family, drummer Malik DOPE, mentalist Max Major, singer Sheldon Riley, singer Nolan Neal, comedian Usama Siddiquee, and dance group and Cowell's Golden Buzzer recipient, W.A.F.F.L.E. Crew.

Next week will be the fourth and final live show before the semifinal round. Season 15 will culminate on Sep. 23, when a winner will be crowned during the scheduled finale. Cowell's participation in the rest of the season has yet to be determined.

A source tells PEOPLE that Cowell has been on track with his recovery.

"Simon's healing has been going well," the source says. "He's recovering at home."

Simon Cowell
Simon Cowell. Jon Kopaloff/FilmMagic

The head judge broke his back on Aug. 8 at his Malibu home when he fell off an electric bike. Hours after the accident, Cowell underwent surgery during which he had a "number of fusions and metal rod" put into his back, a source previously told PEOPLE.

"Get well soon, speedy recovery. And read the manual before getting on the scooter, please," Cowell's Golden Buzzer act joked on Tuesday.

Kelly Clarkson filled in for the first live show, and Kenan Thompson was the second guest judge of the quarterfinals.

On Aug. 15, a friend of Cowell's told PEOPLE that he was "very happy" to have returned home after spending a week in the hospital, where he watched Clarkson serve as guest judge.

Last Tuesday, after the second live show, Vergara told PEOPLE that she misses seeing Cowell next to her week after week.

"It's been great to have all those guest judges, but I do miss Simon. I wish he could've been here," she said. "For me, it's my first time and I feel comfortable when he is with us. Howie and Heidi are amazing, but he's the boss!"

Klum also said that Cowell has been "healing pretty fast."

"I think he's doing amazingly," she added.

America's Got Talent airs Tuesdays and Wednesdays at 8 p.m. ET on NBC.

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