He lives. He had a heart transplant. The heart was given by their friend who died of brain tumor. I think... :P
It is a really hard ending b/c it isn't very clear i think that was done on purpose, he wrote a letter to Mayu, telling her how he imagined their lives, in the end where it shows them and 2 kids indicates that he lived but it was never made clear allowing the readers make up their own mind of whether he died or not.
As for the Heart transplant it was rejected by both Takuma and Kou's family, the surgery he had in the end was an experimental surgery not a heart transplant, because Takuma did not wish to take the heart of someone that wasn't "dead", then you can discuss if you really are dead or not if you are brain dead.
I am not sure who you are talking about, if it is Takuma then i am certain that was on purpose so that the reader could make up their "own" ending, in other words you are never told whether he lived or died so in the manga he never actually died but we don't see him survive the surgery either.
As for Kou that is a whole other matter because he was considered brain dead this actually means you are considered dead since you are unable to stay alive without life support and that your brain has stopped functioning, you can't live without a brain, it is different from country to country how you can be announced brain dead but in most cases several seperate test over time are being made to make sure that the brain is indeed dead, in rare cases it do happen that a person wakes up from such a state, the tests are made to make sure the brain is actually dead, the reason the person afterwards stays on life support is mainly for organ donations, being announced brain dead is the only way a heart can be donated to another person and therefor it is actually really hard getting a new heart, a lot of people die waiting for one, that is why measures to make new hearts artificially so that the need of donor hearts can be reduced and more people will survive. The issue of being brain dead or not and how to make sure is widely discussed, especially because you actually see a beating heart, sign of life.
He didn't receive Kou's heart because he and Kou's family rejected the transplant however he got an experimental heart surgery it was explained in the manga the heart he was to receive was not from a person but was an artificial heart. There have been works on making these kind of heart surgeries i am just not sure how far they actually are with them I think it is something life an life extending treatment rather than a cure but i do know there was talk about a break through not too long ago (long after this manga though).
Also not everyone understands what it means to brain dead and some might even argue if they are actually a life or not, especially when it comes to those left behind, I have never worked at a hospice but I actually do find anatomy and neurology quite interesting, not that i like death very much though.
In the movie and the drama he dies.
i didn't understand the ending, is it him after the surgery or its just his imagination of his future with her ??? someone tell me pleaaaaaaase :(