Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations. (13th December 2012)

• Record Type: Journal Article
• Authors: Wang, Xuan; Ma, Qiaozhen
• Other Names: Cattani Carlo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-12-13
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/714696
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert space D ( A ) × H 2 ( Ω ) ∩ H 0 1 ( Ω ), where the nonlinearity g ( u, t ) is translation compact and the time-dependent external forces h ( x, t ) only satisfy condition (C * ) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.