Pullback attractor for a non-linear evolution equation in elasticity

Abstract

We prove the existence of a pullback attractor for a non{autonomous fourth order evolution equation arising in the fi eld of phase transitions and elasticity theory. The existence of several families of bounded absorbing sets is first proved in several spaces, and owing to the compactness of some inclusions between Sobolev spaces, we can then ensure the existence of a family of compact absorbing sets in the pullback sense and, as a consequence, the existence of a pullback attractor