Premium
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.