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Celeste Corcoran, left, and daughter Sydney Corcoran right discuss their plans for the future a week after the Boston bombings.

A mother and daughter who were severely injured during the Boston Marathon bombings are sharing their hope and gratitude for the lives they still have.

Celeste Corcoran, 47, and her daughter Sydney, 18, hadn't been at the finish line for long, according to Today and NBC's Rock Center. But within a few minutes both of their lives were changed as Celeste lost both of her legs, and Sydney was left with a severed artery.

Husband and father Kevin Corcoran had looked away from his family when he heard the blast, and when he looked back, they were on the ground, family friend Alyssa Carter told ABCNews.com.

It was then that he saw his wife's situation and immediately rushed her to the first aid tents, praying that someone would take care of his daughter, Carter said. Sydney Corcoran's life was saved when three strangers put pressure on her wound, tying a tourniquet around it to stop the bleeding.

But it wasn't until both mother and daughter were in the hospital that they were reunited.

Despite their devastating situation, both mother and daughter have chosen brighter days in the future to focus on. A little over a week after the events, both mother and daughter have begun to discuss what comes next.

"I will have a different life, a different reality," Celeste Corcoran told Today. "But I really believe that if you just kinda persevere and believe in yourself, you really have to dig down deep inside and just be like, 'I can do this.' It's going to be hard, but I can do this."

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Visits from friends and family have lifted their spirits, as well as visits and messages from strangers. Marines from the Semper Fi Fund visited, including an amputee who was placed in a similar situation as Celeste Corcoran.

"He came in here with his legs and I was just amazed," Celeste Corcoran said. "He goes rock climbing. (It) sounds like there's nothing he can't do. Granted, he's a few years younger than I am. But, you know, if you have the spirit and you know that you wanna do it, I can absolutely achieve it."

A video filmed by Carter shows the visit from the Marines in the hospital. During the clip, Celeste Corcoran is heard stating that she never liked to run before because she always would get "the most horrible shin splints."

"So I was like, 'Hey, I don't have shins anymore," Celeste Corcoran said in the video. "I won't be getting shin splints. I can do this."

Boston marathon victim, Jeff Bauman who also had both legs amputated, visited Sydney Corcoran to celebrate her 18th birthday. Other visitors included a local Boston police officer, Shawn Burns who was one of the first to respond to Sydney, as well as Matt Smith, another first responder, and a man who stayed with Sydney Corcoran and brought her help. Both mother and daughter were also surprised by a visit from Hollywood star Bradley Cooper.

A Celeste and Sydney Recovery Fund has been set up with a goal to reach $1,000,000 and has already raised $668,199. The family has health insurance but expenses such as prosthetics may not be covered, and it will be difficult for Celeste Corcoran to return to work as a hairstylist.

Other victims have also received visits from soldiers, and other organizations such as the Tampa area nonprofit 50 Legs.