کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898775 | 1631499 | 2018 | 50 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Exponential stability for the wave model with localized memory in a past history framework
ترجمه فارسی عنوان
پایداری نمایشگاهی برای مدل موج با حافظه محلی در یک چارچوب تاریخ گذشته
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
In this paper we discuss the asymptotic stability as well as the well-posedness of the damped wave equation posed on a bounded domain Ω of Rn,nâ¥2,Ï(x)uttâÎu+â«0âg(s)div[a(x)âu(â
,tâs)]ds+b(x)ut=0, subject to a locally distributed viscoelastic effect driven by a nonnegative function a(x) and supplemented with a frictional damping b(x)â¥0 acting on a region A of Ω, where a=0 in A. Assuming that Ï(x) is constant, considering that the well-known geometric control condition (Ï,T0) holds and supposing that the relaxation function g is bounded by a function that decays exponentially to zero, we prove that the solutions to the corresponding partial viscoelastic model decay exponentially to zero, even in the absence of the frictional dissipative effect. In addition, in some suitable cases where the material density Ï(x) is not constant, it is also possible to remove the frictional damping term b(x)ut, that is, the localized viscoelastic damping is strong enough to assure that the system is exponentially stable. The semi-linear case is also considered.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 11, 5 June 2018, Pages 6535-6584
Journal: Journal of Differential Equations - Volume 264, Issue 11, 5 June 2018, Pages 6535-6584
نویسندگان
M.M. Cavalcanti, V.N. Domingos Cavalcanti, M.A. Jorge Silva, A.Y. de Souza Franco,