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Exponential Stability for a Transmission Problem of a Viscoelastic Wave Equation

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Abstract

This paper is concerned with the study of a transmission problem of viscoelastic waves with hereditary memory, establishing the existence, uniqueness and exponential stability for the solutions of this problem. The proof of the stabilization result combines energy estimates and results due to Gérard (Commun Partial Differ Equ 16:1761–1794 (1991)) on microlocal defect measures.

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Acknowledgements

The authors are thankful to the referees for their suggestions and fruitful comments.

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Authors and Affiliations

  1. Department of Mathematics, State University of Maringá, Maringá, PR, 87020-900, Brazil

    Marcelo M. Cavalcanti, Emanuela R. S. Coelho & Valéria N. Domingos Cavalcanti

Authors
  1. Marcelo M. Cavalcanti
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  2. Emanuela R. S. Coelho
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  3. Valéria N. Domingos Cavalcanti
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Correspondence to Valéria N. Domingos Cavalcanti.

Additional information

Research of Marcelo M. Cavalcanti partially supported by the CNPq Grant 300631/2003-0. Emanuela R. de Sousa Coelho is a Ph.D. student with scholarship supported by CAPES. Research of Valéria N. Domingos Cavalcanti partially supported by the CNPq Grant 304895/2003-2.

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Cavalcanti, M.M., Coelho, E.R.S. & Domingos Cavalcanti, V.N. Exponential Stability for a Transmission Problem of a Viscoelastic Wave Equation. Appl Math Optim 81, 621–650 (2020). https://doi.org/10.1007/s00245-018-9514-9

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