ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM
نویسندگان
چکیده
منابع مشابه
General Decay Rate Estimate for the Energy of a Weak Viscoelastic Equation with an Internal Time-varying Delay Term
In this paper we consider the weak viscoelastic equation with an internal time-varying delay term u tt (x, t)−Δu(x, t)+α(t) t 0 g(t−s)Δu(x, s) ds+a 0 u t (x, t)+a 1 u t (x, t−τ (t)) = 0 in a bounded domain. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general decay rate estimate for the energy, which depends on the behavior of both α and g.
متن کاملFinite time blow up of solutions of the Kirchhoff-type equation with variable exponents
In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.
متن کاملFinite time stabilization of time-delay nonlinear systems with uncertainty and time-varying delay
In this paper, the problem of finite-time stability and finite-time stabilization for a specific class of dynamical systems with nonlinear functions in the presence time-varying delay and norm-bounded uncertainty terms is investigated. Nonlinear functions are considered to satisfy the Lipchitz conditions. At first, sufficient conditions to guarantee the finite-time stability for time-delay nonl...
متن کاملAsymptotic 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...
متن کاملOn the Existence of Solutions of a Nonlocal Elliptic Equation with a p-Kirchhoff-Type Term
Questions on the existence of positive solutions for the following class of elliptic problems are studied: − M ‖u‖p1,p 1,p Δpu f x, u , in Ω, u 0, on ∂Ω, where Ω ⊂ R is a bounded smooth domain, f : Ω ×R → R and M : R → R, R 0,∞ are given functions. Copyright q 2008 F. J. S. A. Corrêa and R. G. Nascimento. This is an open access article distributed under the Creative Commons Attribution License,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: East Asian mathematical journal
سال: 2016
ISSN: 1226-6973
DOI: 10.7858/eamj.2016.030