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Volume 33, Issue 2
Global Solution and Exponential Stability for a Laminated Beam with Fourier Thermal Law

Carlos Raposo, Carlos Nonato, Octavio Paulo Vera Villagran & José Dávalos Chuquipoma

DOI: 10.4208/jpde.v33.n2.4

J. Part. Diff. Eq., 33 (2020), pp. 143-157.

Published online: 2020-05

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  • Abstract

This paper focuses on the long-time dynamics of a thermoelastic laminated beam modeled from the well-established Timoshenko theory. From mathematical point of view, the study system consists of three hyperbolic motion equations coupled with the parabolic equation governed by Fouriers law of heat conduction and, in consequence, does not belong to one of the classical categories of PDE. We have proved the well-posedness and exponential stability of the system. The well-posedness is given by Hille-Yosida theorem. For the exponential decay we applied the energy method by introducing a Lyapunov functional.

  • Keywords

Global solution, laminated beam, Timoshenko, thermoelasticity, energy method.

  • AMS Subject Headings

35B40, 35L53, 74F05, 74F20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

raposo@ufsj.edu.br (Carlos Raposo)

carlos.mat.nonato@hotmail.com (Carlos Nonato)

octaviovera49@gmail.com (Octavio Paulo Vera Villagran)

jadc13@ufsj.edu.br (José Dávalos Chuquipoma)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-33-143, author = {Raposo , CarlosNonato , CarlosVera Villagran , Octavio Paulo and Chuquipoma , José Dávalos}, title = {Global Solution and Exponential Stability for a Laminated Beam with Fourier Thermal Law}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {2}, pages = {143--157}, abstract = {

This paper focuses on the long-time dynamics of a thermoelastic laminated beam modeled from the well-established Timoshenko theory. From mathematical point of view, the study system consists of three hyperbolic motion equations coupled with the parabolic equation governed by Fouriers law of heat conduction and, in consequence, does not belong to one of the classical categories of PDE. We have proved the well-posedness and exponential stability of the system. The well-posedness is given by Hille-Yosida theorem. For the exponential decay we applied the energy method by introducing a Lyapunov functional.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n2.4}, url = {http://global-sci.org/intro/article_detail/jpde/16856.html} }
TY - JOUR T1 - Global Solution and Exponential Stability for a Laminated Beam with Fourier Thermal Law AU - Raposo , Carlos AU - Nonato , Carlos AU - Vera Villagran , Octavio Paulo AU - Chuquipoma , José Dávalos JO - Journal of Partial Differential Equations VL - 2 SP - 143 EP - 157 PY - 2020 DA - 2020/05 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n2.4 UR - https://global-sci.org/intro/article_detail/jpde/16856.html KW - Global solution, laminated beam, Timoshenko, thermoelasticity, energy method. AB -

This paper focuses on the long-time dynamics of a thermoelastic laminated beam modeled from the well-established Timoshenko theory. From mathematical point of view, the study system consists of three hyperbolic motion equations coupled with the parabolic equation governed by Fouriers law of heat conduction and, in consequence, does not belong to one of the classical categories of PDE. We have proved the well-posedness and exponential stability of the system. The well-posedness is given by Hille-Yosida theorem. For the exponential decay we applied the energy method by introducing a Lyapunov functional.

Raposo , CarlosNonato , CarlosVera Villagran , Octavio Paulo and Chuquipoma , José Dávalos. (2020). Global Solution and Exponential Stability for a Laminated Beam with Fourier Thermal Law. Journal of Partial Differential Equations. 33 (2). 143-157. doi:10.4208/jpde.v33.n2.4
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