Exponential stabilization for porous elastic system with one boundary dissipation

Abstract

In this paper, we consider the one-dimensional porous elastic system with mixed dissipation term at the point \(x=0\) acting only on the volumetric fraction of the system. We prove that the operator \({\mathcal {A}}\) associated with the problem is an infinitesimal generator of a \(C_0\)–semigroup of contractions and we prove the exponential stability if an important restriction is imposed on the constitutive coefficients.

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Acknowledgements

The authors are grateful to the anonymous referee for its constructive remarks which have enhanced the presentation of this paper. Moreover, we are grateful to the professors Edson de Andrade Araújo and Pedro Tupã Pandava Aum of the Faculty of Petroleum Engineering of the Federal University of Pará for necessary support to make real the present present work. We also say many thanks to PROPESP/UFPA.

Funding

D.S. Almeida Júnior thanks the CNPq for financial support through the following projects:

\(\bullet \)“New guidelines for dissipative Timoshenko type systems at light of the second spectrum” - CNPq Grant 310423/2016-3 and “Stabilization for Timoshenko systems from the second spectrum point of view” - PNPD /CAPES/INCTMAT/LNCC 88887.351763/2019-00.

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Correspondence to A. J. A. Ramos.

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Ramos, A.J.A., Júnior, D.S.A., Freitas, M.M. et al. Exponential stabilization for porous elastic system with one boundary dissipation. Ann Univ Ferrara 66, 113–134 (2020). https://doi.org/10.1007/s11565-019-00334-1

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Keywords

  • Porous-elasticity
  • Boundary feedback
  • Asymptotic behavior

Mathematics Subject Classification

  • 35B35
  • 35Q74
  • 74H40
  • 74K10
  • 93D15