| Full text | |
| 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 |