#### Vol. 301, No. 2, 2019

 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 ${ℝ}^{N}$, $N\ge 2$. 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

$\left\{\begin{array}{cc}{u}_{tt}+{\Delta }^{2}u+a\Delta \theta =f\left(u\right),\phantom{\rule{1em}{0ex}}\hfill & t>\tau ,x\in \Omega ,\hfill \\ {\theta }_{t}-\kappa \left(t\right)\Delta \theta -a\Delta {u}_{t}=0,\phantom{\rule{1em}{0ex}}\hfill & t>\tau ,x\in \Omega ,\hfill \end{array}\right\$

subject to boundary conditions

$u=\Delta u=\theta =0,\phantom{\rule{1em}{0ex}}t>\tau ,\phantom{\rule{1em}{0ex}}x\in \partial \Omega ,$

with respect to the functional parameter $\kappa$.

##### Keywords
pullback attractors, regularity, thermoelastic plate systems, upper semicontinuity
##### Mathematical Subject Classification 2010
Primary: 35B40, 35B41, 35B65, 37B55