Flattening Property and the Existence of Global Attractors in Banach Space

This paper analyses the existence of global attractor in infinite dimensional system using flattening property. The earlier stage we show the existence of the global attractor in complete metric space by using concept of the w-limit compact concept with measure of non compactness methods. Then we show that the w-limit compact concept is equivalent with the flattening property in Banach space. If we can prove there exist an absorbing set in the system and the flattening property holds, then the global attractor exist in the system.