He is alive. The mangaka, Aoki-sensei had stated this after many fans asked her.

I don;'t think we know how it ended. I really hate plots like this. All the guy really did was cause both of them more grief and sadness. Even if he doesn't live part 20, I think she would be happier in the long run knowing that she was there for him and they had a good relationship together. The way it stands now , If he does die at 20, then her memories of him are filled with a ton of drama, years of mixed messages, and lots of sadness. He may of thought he was being selfless, but he was really just being a d$%k.

On a side note, in real life when people find out they may not have long to live, they usually become more emotional and want to spend more time with their loved ones. The usually don't try to drive them away.

I don't know why the artist couldn't give us a proper ending. Japanese authors are really into these fuzzy type of endings. It's almost rare to get a satisfying ending in manga. After investing the time into reading 10+ volumes, I want to know what really happens. I don't want some ambiguous ending that leaves it to my imagaination.

Jeffrey