کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899142 1631511 2017 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Convergence to equilibrium of solutions to a nonautonomous semilinear viscoelastic equation with finite or infinite memory
ترجمه فارسی عنوان
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موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
In this paper we consider the nonautonomous semilinear viscoelastic equationutt−Δu+∫0τk(s)Δu(t−s)ds+f(x,u)=g,τ∈{t,∞}, in R+×Ω, with Dirichlet boundary conditions and finite (τ=t) or infinite (τ=∞) memory. Here Ω is a bounded domain in Rn with smooth boundary and the nonlinearity f:Ω×R+→R is analytic in the second variable, uniformly with respect to the first one. For this equation, we derive an appropriate Lyapunov function and we use the Łojasiewicz-Simon inequality to show that the dissipation given by the memory term is strong enough to prove the convergence to a steady state for any global bounded solution. In addition, we discuss the rate of convergence to equilibrium which is polynomial or exponential, depending on the Łojasiewicz exponent and the decay of the time-dependent right-hand side g.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 263, Issue 11, 5 December 2017, Pages 7322-7351
نویسندگان
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