Regularity and upper semicontinuity of pullback attractors for a class of nonautonomous thermoelastic plate systems

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 $ℝ^{N}$ , $N \geq 2$ . 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

\{\begin{matrix} u_{t t} + Δ^{2} u + a Δ θ = f (u), & t > τ, x \in Ω, \\ θ_{t} - κ (t) Δ θ - a Δ u_{t} = 0, & t > τ, x \in Ω, \end{matrix}

subject to boundary conditions

u = Δ u = θ = 0, t > τ, x \in \partial Ω,

with respect to the functional parameter $κ$ .

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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

Vol. 301, No. 2, 2019

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

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors