Attractors for the strongly damped wave equation with p‐Laplacian. (18th January 2017) - Khanmamedov, Azer; Sen, Zehra
Abstract : This paper is concerned with the initial‐boundary value problem for one‐dimensional strongly damped wave equation involving p ‐Laplacian. For p  > 2, we establish the existence of weak local attractors for this problem in W 0 1, p ( 0, 1 ) × L 2 ( 0, 1 ) . Under restriction 2 <  p  < 4, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in W 0 1, p ( 0, 1 ) × L 2 ( 0, 1 ), and this attractor is a bounded subset of W 1, ∞ ( 0, 1 ) × W 1, ∞ ( 0, 1 ) . Copyright © 2017 John Wiley & Sons, Ltd.