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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.)

PULLBACK ATTRACTORS FOR A CLASS OF NON-AUTONOMOUS THERMOELASTIC PLATE SYSTEMS

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Author(s):
Bezerra, Flank D. M. [1] ; Carbone, Vera L. [2] ; Nascimento, Marcelo J. D. [2] ; Schiabel, Karina [2]
Total Authors: 4
Affiliation:
[1] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba - Brazil
[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 23, n. 9, p. 3553-3571, NOV 2018.
Web of Science Citations: 2
Abstract

In this article we study the asymptotic behavior of solutions, in the sense of pullback attractors, of the evolution system [u(tt) + Delta(2)u + a(t)Delta theta = f(t,u), t > tau, x is an element of Omega, theta(t) + kappa Delta theta + a(t)Delta u(t) = 0, t > tau, x is an element of Omega, subject to boundary conditions u = Delta u= theta = 0, t > tau, x is an element of partial derivative Omega, where Omega is a bounded domain in R-N with N >= 2, which boundary partial derivative Omega is assumed to be a C-4-hypersurface, kappa > 0 is constant, a is an Holder continuous function and f is a dissipative nonlinearity locally Lipschitz in the second variable. Using the theory of uniform sectorial operators, in the sense of P. Sobolevskii ({[}23]), we give a partial description of the fractional power spaces scale for the thermoelastic plate operator and we show the local and global well-posedness of this non-autonomous problem. Furthermore we prove existence and uniform boundedness of pullback attractors. (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