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Global attractor for suspension bridge equations with memory
Author(s) -
Kang JumRan
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3520
Subject(s) - suspension (topology) , attractor , bridge (graph theory) , uniqueness , bounded function , mathematics , domain (mathematical analysis) , partial differential equation , mathematical analysis , pure mathematics , medicine , homotopy
This paper is concerned with a suspension bridge equation with memory effectsu tt + α Δ 2 u − ∫ 0 ∞ μ ( s ) Δ 2 u ( t − s ) ds + k u + + f ( u ) = h ( x ) , defined in a bounded domain ofR N . For the suspension bridge equation without memory, there are many classical results. Existing results mainly devoted to existence and uniqueness of a weak solution, energy decay of solution and existence of global attractors. However the existence of global attractors for the suspension bridge equation with memory was no yet considered. The object of the present paper is to provide some results on the well‐posedness and long‐time behavior to the suspension bridge equation in a more with past history. Copyright © 2015 John Wiley & Sons, Ltd.