Long‐time behavior of a nonlinear viscoelastic beam equation with past history | Zendy

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Long‐time behavior of a nonlinear viscoelastic beam equation with past history

Author(s) -

Narciso Vando

Publication year - 2014

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.3109

Subject(s) - viscoelasticity , attractor , nonlinear system , mathematics , beam (structure) , term (time) , mathematical analysis , mathematical physics , physics , thermodynamics , quantum mechanics , optics

This paper is concerned with the existence of a global attractor for the nonlinear viscoelastic beam equation with past history memoryu tt + k Δ 2 u − ∫ − ∞ t μ ( t − τ )Δ 2 u ( τ ) dτ + f ( u ) + g (u t) = h ,where g ( u t ) is a damping like | u t | r u t and f ( u ) is a source term like | u | α u − | u | β u , by considering 0 ≤ β < α and r > 0. Copyright © 2014 John Wiley & Sons, Ltd.

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