Siberian Mathematical Journal

, Volume 47, Issue 1, pp 45–54 | Cite as

On One Class of Systems of Differential Equations and on Retarded Equations

  • G. V. Demidenko
  • V. A. Likhoshvai
  • T. V. Kotova
  • Yu. E. Khropova
Article

Abstract

We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis.

Keywords

retarded differential equations weak solution 

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References

  1. 1.
    Likhoshvai V. A., Fadeev S. I., Demidenko G. V., and Matushkin Yu. G., “Modeling by a delay equation of multiphase synthesis without bifurcation,” Sibirsk. Zh. Industr. Mat., 7, No.1, 73–94 (2004).MathSciNetGoogle Scholar
  2. 2.
    Demidenko G. V., Kolchanov N. A., Likhoshvai V. A., Matushkin Yu. G., and Fadeev S. I., “Mathematical modeling of regulator contours of gene nets,” Zh. Vychisl. Mat. i Mat. Fiziki, 44, No.12, 2276–2295 (2004).MathSciNetGoogle Scholar
  3. 3.
    Demidenko G. V. and Likhoshvai V. A., “On differential equations with retarded argument,” Siberian Math. J., 46, No.3, 417–430 (2005).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • G. V. Demidenko
    • 1
  • V. A. Likhoshvai
    • 2
  • T. V. Kotova
    • 3
  • Yu. E. Khropova
    • 3
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Institute of Cytology and GeneticsNovosibirskRussia
  3. 3.Novosibirsk State UniversityNovosibirskRussia

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