کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609880 1338532 2016 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Attractors for wave equations with degenerate memory
ترجمه فارسی عنوان
جذب برای معادلات موج با حافظه منحرف
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

This paper is concerned with the long-time dynamics of a semilinear wave equation with degenerate viscoelasticityutt−Δu+∫0∞g(s)div[a(x)∇u(t−s)]ds+f(u)=h(x), defined in a bounded domain Ω of R3R3, with Dirichlet boundary condition and nonlinear forcing f(u)f(u) with critical growth. The problem is degenerate in the sense that the function a(x)≥0a(x)≥0 in the memory term is allowed to vanish in a part of Ω‾. When a(x)a(x) does not degenerate and g   decays exponentially it is well-known that the corresponding dynamical system has a global attractor without any extra dissipation. In the present work we consider the degenerate case by adding a complementary frictional damping b(x)utb(x)ut, which is in a certain sense arbitrarily small, such that a+b>0a+b>0 in Ω‾. Despite that the dissipation is given by two partial damping terms of different nature, none of them necessarily satisfying a geometric control condition, we establish the existence of a global attractor with finite-fractal dimension.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 260, Issue 1, 5 January 2016, Pages 56–83
نویسندگان
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