Does Ivan Denisovich Shukhov represent a character who is willing to survive? What does camp life in the novel illustrate to us about surviving the Gulag?

Ivan Denisovich Shukhov very much wants to survive. He uses numerous strategies to increase the likelihood of his survival; these efforts occupy him constantly. For example, he wakes up early, before roll call, as that is a time when he can make an effort to do things for the guards so that they might treat him better in return, or pick up a small job that might earn him some extra food or privilege later.

He could bring one of the big gang bosses his dry felt boots while he was still in his bunk . . . Or he could run around to one of the supply rooms where there might be a little job, sweeping or carrying something.

Shukhov learns to value even what seem like the smallest things because they can rarely be replaced. He holds onto his spoon above all, carrying it around in his boot. When he goes outside to the well, he must rush off: “He'd had to get ready . . . in a hurry, but he still hadn't forgotten his spoon.”
As depicted in the novel, camp life is a constant struggle to survive. The Gulag is a harsh physical environment, and the prisoners are discouraged and depressed as well as cold and hungry. One's initial sentence does not matter, because additional years can always be tacked on. Dignity and self-possession are important skills, as shown by the long-term inmate who sits ramrod straight to drink his soup; he cannot eat, because he has lost his teeth, but he refuses to be bowed:

This old man’d been in camps and prisons more years than you could count and had never come under any amnesty. When one ten-year stretch was over they slapped on another . . . In the camp you could pick him out among all the men with their bent backs because he was straight as a ramrod. When he sat at the table it looked like he was sitting on something to raise himself up higher.

Prisoners form friendships because they cannot survive totally alone. Still, they are always wary, as they know alliances can shift. Kurzyomin, a long-term prisoner, advises keeping to oneself and not telling tales.

It's the law of the taiga here, men, but a man can live here, just like anywhere else. Know who croaks first? The guy who licks out bowls, put his faith in the sick bay, or squeals to the godfather.