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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.)

A class of dissipative nonautonomous nonlocal second-order evolution equations

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Author(s):
Bezerra, F. D. M. ; Nascimento, M. J. D. ; da Silva, S. H.
Total Authors: 3
Document type: Journal article
Source: APPLICABLE ANALYSIS; v. 96, n. 13, p. 2180-2191, 2017.
Web of Science Citations: 2
Abstract

In this paper we consider the following nonlinear and spatially nonlocal second-order evolution equation from nonlocal theory of continuum mechanics [u(tt) + a(t, x) u(t) - integral(RN) J(x, y)(beta u(y) - u(x)) dy = f (u), x is an element of Omega, t > tau, u(x, tau) = u(0)(x), u(tau) (x, tau) = u(1)(x), x is an element of Omega, u(x, t) = 0, x is an element of R-n\textbackslash{}Omega, t >= tau, where Omega is a bounded smooth domain in R-n, n >= 3, 0 < beta < 1, and a is a bounded continuous function. Here, the kernel J is a nonnegative, symmetric bounded function with bounded derivative, satisfying certain growth conditions. We deduce an energy functional associated to these problem, and we study the local and global well posedness, boundedness and asymptotic behavior of its solutions. Additionally we study the stability of the trivial solution associated to these problem. (AU)

FAPESP's process: 14/03109-6 - Dynamics of autonomous and nonautonomous semilinear problems
Grantee:Marcelo José Dias Nascimento
Support type: Regular Research Grants
FAPESP's process: 14/03686-3 - The dynamics of evolution equations governed by fractional powers of closed operators
Grantee:Flank David Morais Bezerra
Support type: Scholarships in Brazil - Post-Doctorate