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Global attractors for the viscous hyperelastic‐rod wave equation
Author(s) -
Yu Shengqi
Publication year - 2012
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.2668
Subject(s) - hyperelastic material , attractor , mathematics , divergence (linguistics) , mathematical analysis , term (time) , wave equation , viscous liquid , differential equation , operator (biology) , forcing (mathematics) , finite element method , mechanics , physics , linguistics , philosophy , biochemistry , chemistry , repressor , quantum mechanics , gene , transcription factor , thermodynamics
We consider the viscous hyperelastic‐rod wave equation subject to an external force, where the viscous term is given by second order differential operator in divergence form. Under some mild assumptions on the viscous term, first, we establish the global well‐posedness in both the periodic case and the case of the whole line, afterwards, we show the existence of global attractors for the two cases, respectively. Copyright © 2012 John Wiley & Sons, Ltd.