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SeMA Journal

, Volume 61, Issue 1, pp 1–17 | Cite as

Control of coupled parabolic systems and Diophantine approximations

  • Florian Luca
  • Luz de TeresaEmail author
Article

Abstract

In this paper we consider the boundary null controllability problem of two coupled one dimensional parabolic equations. We show that in the case in which each equation have different diffusion constant, lets say \(\nu \) and 1, the null controllability result depends on the nature of the diffusion constant \(\nu \). Using rational approximations of the number \(\nu \), we show that null controllability is possible or not. In this sense the result is a number theoretical result.

Keywords

Null controllability Observability inequality Rational approximations 

Mathematics Subject Classification (2000)

93C20 11A55 

Notes

Acknowledgments

The authors want to thank the anonymous referee for his/her suggestions and corrections that greatly improved the paper.

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Copyright information

© Sociedad Española de Matemática Aplicada 2013

Authors and Affiliations

  1. 1.Fundación Marcos MoshinskyInstituto de Ciencias Nucleares UNAMMexico, DFMexico
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Circuito Exterior, C.U.Mexico, DFMexico

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