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Decay Structures for the Equations of Porous Elasticity in One-Dimensional Whole Space

  • Ramón Quintanilla
  • Yoshihiro UedaEmail author
Article
  • 23 Downloads

Abstract

This paper investigates the solutions of the porous-elastic materials with dissipation in the case of the whole real line. We consider three different cases. First we consider the case when there are dissipation mechanisms at the elastic structure and the porous structure and we prove the decay structure is standard type. Second we consider the cases when the dissipation is only on the elastic structure or on the porous structure. In these cases we show that the decay structure is regularity-loss type. Furthermore, we will show the optimality for the decay estimates for all cases.

Keywords

Stability analysis Decay estimates Regularity-loss structure Cauchy problem 

Notes

Acknowledgements

The work of the first author is supported by project “Análisis Matemático de Problemas de la Termomecánica” (MTM2016-74934-P), (AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness. The work of the second author is supported by Grant-in-Aid for Scientific Research (C) No. 18K03369 from Japan Society for the Promotion of Science.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPolytechnic University of CataloniaTerrassaSpain
  2. 2.Faculty of Maritime SciencesKobe UniversityKobeJapan

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