Vol. 301, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Regularity and upper semicontinuity of pullback attractors for a class of nonautonomous thermoelastic plate systems

Flank D. M. Bezerra, Vera L. Carbone, Marcelo J. D. Nascimento and Karina Schiabel

Vol. 301 (2019), No. 2, 395–419
DOI: 10.2140/pjm.2019.301.395
Abstract

We study the long-time dynamics, in the sense of pullback attractors, of solutions for semilinear nonautonomous thermoelastic plate systems in a bounded smooth domain in N, N 2. Using the theory of uniform sectorial operators, in the sense of P. Sobolevskiĭ (1961), we will prove existence, uniform boundedness, regularity and upper semicontinuity of pullback attractors for the evolution system

utt + Δ2u + aΔθ = f(u),t > τ, x Ω, θt κ(t)Δθ aΔut = 0, t > τ, x Ω,

subject to boundary conditions

u = Δu = θ = 0,t > τ,x Ω,

with respect to the functional parameter κ.

Keywords
pullback attractors, regularity, thermoelastic plate systems, upper semicontinuity
Mathematical Subject Classification 2010
Primary: 35B40, 35B41, 35B65, 37B55
Milestones
Received: 27 September 2018
Revised: 12 January 2019
Accepted: 17 January 2019
Published: 24 October 2019
Authors
Flank D. M. Bezerra
Departamento de Matemática
Universidade Federal da Paraíba
Cidade Universitária
João Pessoa-PB
Brazil
Vera L. Carbone
Departamento de Matemática
Universidade Federal de São Carlos
São Carlos
Brazil
Marcelo J. D. Nascimento
Departamento de Matemática
Universidade Federal de São Carlos
São Carlos
Brazil
Karina Schiabel
Departamento de Matemática
Universidade Federal de São Carlos
São Carlos
Brazil