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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Attractors for wave equations with degenerate memory

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Author(s):
Cavalcanti, M. M. [1] ; Fatori, L. H. [2] ; Ma, T. F. [3]
Total Authors: 3
Affiliation:
[1] Univ Estadual Maringa, Dept Math, BR-87020900 Maringa, Parana - Brazil
[2] Univ Estadual Londrina, Dept Math, BR-86057970 Londrina, PR - Brazil
[3] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Journal of Differential Equations; v. 260, n. 1, p. 56-83, JAN 5 2016.
Web of Science Citations: 6
Abstract

This paper is concerned with the long-time dynamics of a semilinear wave equation with degenerate is viscoelasticity utt - Delta u + integral(infinity)(0) g(s)div{[}a(x)del u(t - s)]ds + f(u) = h(x), defined in a bounded domain Omega of R-3, with Dirichlet boundary condition and nonlinear forcing f (u) with critical growth. The problem is degenerate in the sense that the function a(x) >= 0 in the memory term is allowed to vanish in a part of Omega. When 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)u(t), which is in a certain sense arbitrarily small, such that a + b > 0 in Omega. 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. (C) 2015 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 14/08767-1 - Frictional versus viscoelastic models with history
Grantee:Ma To Fu
Support type: Research Grants - Visiting Researcher Grant - Brazil
FAPESP's process: 12/19274-0 - Asymptotic dynamics for autonomous and nonautonomous nonlinear wave equations
Grantee:Ma To Fu
Support type: Regular Research Grants