Attractors for the strongly damped wave equation with p‐Laplacian. (18th January 2017)

• Record Type: Journal Article
• Authors: Khanmamedov, Azer; Sen, Zehra
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 12(2017)
• Page Start: 4436
• Page End: 4447
• Publication Date: 2017-01-18
• Subjects: wave equation -- p‐Laplacian -- attractors; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4315
• Languages: English
• ISSNs: 0170-4214

Abstract

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.