American Institute of Mathematical Sciences

Advanced
January  2010, 9(1): 161-192. doi: 10.3934/cpaa.2010.9.161

Asymptotic behavior of thermoviscoelastic Berger plate

Mykhailo Potomkin 1,

1. 

Kharkiv National University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkiv, Ukraine

Received  January 2009 Revised  May 2009 Published  October 2009

System of partial differential equations with convolution terms and non-local nonlinearity describing oscillations of plate due to Berger's approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and fading memory of material is considered. The equation is transformed into a dynamical system in a suitable Hilbert space, which asymptotic behavior is analysed. Existence of a compact global attractor in this dynamical system and some of its properties are proved in this paper. Main tool in analysis of asymptotic behavior is stabilizability inequality.
Keywords: global attractor, linear memory., Coupled PDE system.
Mathematics Subject Classification: 35B40, 35B4.
Citation: Mykhailo Potomkin. Asymptotic behavior of thermoviscoelastic Berger plate. Communications on Pure and Applied Analysis, 2010, 9 (1) : 161-192. doi: 10.3934/cpaa.2010.9.161
[1]

Roberto Triggiani. The coupled PDE system of a composite (sandwich) beam revisited. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 285-298. doi: 10.3934/dcdsb.2003.3.285
[2]

Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control and Related Fields, 2021, 11 (3) : 601-624. doi: 10.3934/mcrf.2021014
[3]

Moncef Aouadi, Alain Miranville. Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Evolution Equations and Control Theory, 2015, 4 (3) : 241-263. doi: 10.3934/eect.2015.4.241
[4]

Vanessa Baumgärtner, Simone Göttlich, Stephan Knapp. Feedback stabilization for a coupled PDE-ODE production system. Mathematical Control and Related Fields, 2020, 10 (2) : 405-424. doi: 10.3934/mcrf.2020003
[5]

Sandesh Athni Hiremath, Christina Surulescu, Anna Zhigun, Stefanie Sonner. On a coupled SDE-PDE system modeling acid-mediated tumor invasion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2339-2369. doi: 10.3934/dcdsb.2018071
[6]

George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 817-833. doi: 10.3934/dcds.2008.22.817
[7]

Maria Laura Delle Monache, Paola Goatin. A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 435-447. doi: 10.3934/dcdss.2014.7.435
[8]

Marilena N. Poulou, Nikolaos M. Stavrakakis. Global attractor for a Klein-Gordon-Schrodinger type system. Conference Publications, 2007, 2007 (Special) : 844-854. doi: 10.3934/proc.2007.2007.844
[9]

Francesca Bucci, Igor Chueshov, Irena Lasiecka. Global attractor for a composite system of nonlinear wave and plate equations. Communications on Pure and Applied Analysis, 2007, 6 (1) : 113-140. doi: 10.3934/cpaa.2007.6.113
[10]

Olivier Goubet, Manal Hussein. Global attractor for the Davey-Stewartson system on $\mathbb R^2$. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1555-1575. doi: 10.3934/cpaa.2009.8.1555
[11]

Jia-Cheng Zhao, Zhong-Xin Ma. Global attractor for a partly dissipative reaction-diffusion system with discontinuous nonlinearity. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022103
[12]

Brahim Alouini. Finite dimensional global attractor for a class of two-coupled nonlinear fractional Schrödinger equations. Evolution Equations and Control Theory, 2022, 11 (2) : 559-581. doi: 10.3934/eect.2021013
[13]

Salah Missaoui, Ezzeddine Zahrouni. Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system with cubic nonlinearities in $\mathbb{R}^2$. Communications on Pure and Applied Analysis, 2015, 14 (2) : 695-716. doi: 10.3934/cpaa.2015.14.695
[14]

George Avalos, Roberto Triggiani. Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 417-447. doi: 10.3934/dcdss.2009.2.417
[15]

Rong Chen, Shihang Pan, Baoshuai Zhang. Global conservative solutions for a modified periodic coupled Camassa-Holm system. Electronic Research Archive, 2021, 29 (1) : 1691-1708. doi: 10.3934/era.2020087
[16]

Jason Metcalfe, David Spencer. Global existence for a coupled wave system related to the Strauss conjecture. Communications on Pure and Applied Analysis, 2018, 17 (2) : 593-604. doi: 10.3934/cpaa.2018032
[17]

Takashi Narazaki. Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations. Conference Publications, 2009, 2009 (Special) : 592-601. doi: 10.3934/proc.2009.2009.592
[18]

Salah Missaoui. Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system in $ \mathbb{R}^3 $ nonlinear KGS system. Communications on Pure and Applied Analysis, 2022, 21 (2) : 567-584. doi: 10.3934/cpaa.2021189
[19]

Bin Li. On the blow-up criterion and global existence of a nonlinear PDE system in biological transport networks. Kinetic and Related Models, 2019, 12 (5) : 1131-1162. doi: 10.3934/krm.2019043
[20]

Bo You. Global attractor of the Cahn-Hilliard-Navier-Stokes system with moving contact lines. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2283-2298. doi: 10.3934/cpaa.2019103

2021 Impact Factor: 1.273

Tools

Metrics

  • PDF downloads (82)
  • HTML views (0)
  • Cited by (21)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy