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Dynamics of Nonlinear Parabolic Equations with Cosymmetry

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Computer Algebra in Scientific Computing (CASC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4770))

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Abstract

Dynamics of a cosymmetric system of nonlinear parabolic equations is studied to model of population kinetics. Computer algebra system Maple is applied to perform some stages of analytical investigation and develop a finite-difference scheme which respects the cosymmetry property. We present different scenarios of evolution for coexisted nonstationary regimes and families of equilibria branched off of the state of rest.

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References

  1. Yudovich, V.I.: Cosymmetry, degeneration of solutions of operator equations, and the onset of filtration convection. Mat. Zametki. 49, 142–148 (1991)

    MathSciNet  Google Scholar 

  2. Yudovich, V.I.: Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it. Chaos. 5, 402–411 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Murray, J.D.: Mathematical biology, p. 766. Springer, New York (1993)

    MATH  Google Scholar 

  4. Frischmuth, K., Tsybulin, V.G.: Cosymmetry preservation and families of equilibria. In: Computer Algebra in Scientific Computing – CASC 2004, pp. 163–172 (2004)

    Google Scholar 

  5. Frischmuth, K., Tsybulin, V.G.: Families of equilibria and dynamics in a population kinetics model with cosymmetry. Physics Letters A 338, 51–59 (2005)

    Article  MATH  Google Scholar 

  6. Govorukhin, V.N.: Calculation of one-parameter families of stationary regimes in a cosymmetric case and analysis of plane filtrational convection problem. Continuation methods in fluid dynamics, Notes Numer. Fluid Mech. Vieweg. Braunschweig 74, 133–144 (2000)

    MathSciNet  Google Scholar 

  7. Frischmuth, K., Tsybulin, V.G.: Computation of a family of non-cosymmetrical equilibria in a system of two nonlinear parabolic equations. Computing 16, 67–82 (2002)

    MathSciNet  Google Scholar 

  8. Yudovich, V.I.: Bifurcations under perturbations violating cosymmetry. Doklady Physics 49(9), 522–526 (2004)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computational Mathematics, Southern Federal University, Rostov-na-Donu, Russia

    Ekaterina S. Kovaleva & Vyacheslav G. Tsybulin

  2. Department of Mathematics, University of Rostock, Germany

    Kurt Frischmuth

Authors
  1. Ekaterina S. Kovaleva
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  2. Vyacheslav G. Tsybulin
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  3. Kurt Frischmuth
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Editor information

Victor G. Ganzha Ernst W. Mayr Evgenii V. Vorozhtsov

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© 2007 Springer-Verlag Berlin Heidelberg

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Kovaleva, E.S., Tsybulin, V.G., Frischmuth, K. (2007). Dynamics of Nonlinear Parabolic Equations with Cosymmetry. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2007. Lecture Notes in Computer Science, vol 4770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75187-8_21

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  • DOI: https://doi.org/10.1007/978-3-540-75187-8_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75186-1

  • Online ISBN: 978-3-540-75187-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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