Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type
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چکیده
منابع مشابه
Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type
Received 3 June 2012; Accepted 17 July 2012 Academic Editor: Yongkun Li Copyright q 2012 Nasser-Eddine Tatar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A wave equation of the Kirchhoff type with several nonlinearities is sta...
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Global Existence and Asymptotic Behavior for a Nonlinear Viscoelastic Problem
In this paper the nonlinear viscoelastic wave equation |ut|utt −∆u−∆utt + ∫ t 0 g(t− τ)∆u(τ)dτ − γ∆ut = b|u|p−2u is considered. Using the potential well method a global existence and an exponential decay result are proved. Moreover, for sufficiently large values of the initial data and for a suitable relation between p and the relaxation function g, we establish an unboundedness result.
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15 صفحه اولAsymptotic behavior for a nonlinear viscoelastic problem with a velocity-dependent material density
where Ω is a bounded domain in Rn, n≥ 1, with a smooth boundary Γ. The real number ρ is assumed to satisfy 0 < ρ ≤ 2/(n− 2) if n ≥ 3 or ρ > 0 if n= 1,2. The function g(t) is positive and will be specified further below. This model appears in viscoelasticity. We are in the case where the material density depends on ut (see [5, 11]). In [1], Cavalcanti et al. studied this nonlinear problem (ρ > 0...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2012
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2012/936140