Analysis:Does History Change

In order not to change history
In order to not change history, Yuni recreates the past history. The reason he had to be sure history didn't change was discussed in the main story and is listed below:
 * Yuni follows the same history
 * The satellite phone connects on January 16th
 * The rescue team arrives on January 17 as a result of the call
 * The airplane accident is reported on January 17
 * Yukidoh (Sunglasses) sees the report and makes Mount Akakura the new stage for the Yukidoh Plan. (Originally it was supposed to be in Australia when he wanted to travel on January 18)
 * Using Mount Akakura as the stage for the Yukidoh Plan, transfers occur on Mount Akakura
 * Because of the space time transfers, Kokoro and the others are rescued

2011 for the Yuni of 2012
In order to change the history where Kokoro and the others died in the avalanche, Yuni took the risk and went to the cabin.

But Yuni says "History won't change"

The Yuni of 2012 should have experienced the following in 2011: "Kokoro and the others were swallowed by the avalanche"

But if they were rescued, history should have definitely changed.

On top of that, Yuni says the newspaper and magazine in Satoru's room might be fake...

If the newspaper is Yuni's work, what kind of history did Yuni experience? Just like Satoru's good end, it's very likely his history is the one where Kokoro and the others were saved because of the space-time transfer.

However, Yuni is evasive. The newspapers may have been fake, or maybe not.

The Yuni of 2012 has experienced 2011. No matter how hard you try to find the answer, you'll never find it.

Kokoro may have died in the avalanche, she may have been saved using the space-time transfers, she may have died when the plane crashed.

In the end, it's another mystery with many differing possibilities.

The answer is uncertain. It seems there's no single solution.

2011 for Utsumi
In 2012, Utsumi says that "Fuyukawa Kokoro is already dead". She also makes comments like "Kokoro died in an avalanche"

Of course, that doesn't mean that Utsumi soley relied on the newspaper and magazine. Perhaps she had another source of information. If what Utsumi is saying is true, the avalanche will actually happen. Does this contradict the conclusion of the previous section?

We can solve this problem with the terabyte disk.

Utsumi learns from the terabyte disk that Satoru has DID. In that case, did it also say that Kokoro and the others died in the avalanche? And if it did, was the disk really telling the truth? Regardless, she became convinced that they really did die in the avalanche.

Many Worlds Interpretation
It's honestly meaningless to ask whether or not history changed.

The world of Remember 11 follows the Many Worlds Interpretation. There is a new world each time the player goes through the game.

Making a new choice doesn't change the history of the current world. If different actions happened in the past, that's because you're in a "different world".

For that reason, we can't be sure if 2011 and 2012 occur in the same world. Returning to 2011 doesn't put you back in the same world as 2012.

If you jump back temporarily after a wrong decision and choose a different action, it becomes a different world at that moment.

Worlds that affect each other
It was written before that the Kokoro and Satoru routes affect each other as follow:

Kokoro Route -> Satoru Route -> Kokoro Route -> Satoru Route -> ...

Here, both the Kokoro and Satoru routes are stories in different worlds. It becomes more obvious when you consider the last transfer in the "final level".

But if they occur in different worlds, why do they affect each other? Information from Kokoro's path is transmitted to Satoru's, and information from Satoru's path is transmitted to Kokoro's.

This is probably the effect of the player. The memory of the player is what connects the worlds to each other. The memory of the player decides which world you will experience.

Summary

 * History doesn't change becuase each change creates a NEW world which doesn't affect the old one.
 * It's impossible to determine if Kokoro died in the avalanche when playing in 2012 since the player is jumping not only through time, but also between worlds.