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Global attractors for the coupled suspension bridge system with temperature
Author(s) -
Dell'Oro Filippo,
Giorgi Claudio
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.3526
Subject(s) - suspension (topology) , attractor , dissipation , semigroup , mathematics , thermoelastic damping , nonlinear system , bridge (graph theory) , string (physics) , term (time) , domain (mathematical analysis) , argument (complex analysis) , mathematical analysis , thermal , pure mathematics , mathematical physics , physics , thermodynamics , medicine , biochemistry , chemistry , quantum mechanics , homotopy
This paper deals with the long‐term properties of the thermoelastic nonlinear string‐beam system related to the well‐known Lazer–McKenna suspension bridge model 0.1u tt + u xxxx − ( β + ∥ u x∥L 2 ( 0 , 1 ) 2 ) u xx + ( u − v ) + + θ xx = fv tt − v xx − ( u − v ) + + ϕ x = gθ t − θ xx − u txx = hϕ t − ϕ xx + v tx = 0 .In particular, no mechanical dissipation occurs in the equations, because the loss of energy is entirely due to thermal effects. The existence of regular global attractors for the associated solution semigroup is proved (without resorting to a bootstrap argument) for time‐independent supplies f , g , h and any β ∈ R . Copyright © 2015 John Wiley & Sons, Ltd.