Analysis of the long-time asymptotic behaviour of the solution of a two-dimensional reaction-diffusion equation

  • Authors

    • Joel Ndam University of Jos
    2015-04-20
    https://doi.org/10.14419/ijamr.v4i2.4426
  • Reaction-diffusion equation, Energy function, Poincare inequality, Reflecting boundary conditions.

  • A reaction-diffusion equation in two dimensions is considered. The long-time asymptotic behaviour of the solution of this equation is examined in terms of uniform diffusion as well as density-dependent diffusion. The results show that in both cases, the solution attains a steady state, but does so more slowly with the variable diffusion coefficient when its magnitude d<1.

  • References

    1. [1] D. S. Jones and B.D. Sleeman, Differential Equations and Mathematical Biology, Chapman and Hall/CRC, USA, 2003.

      [2] L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Springer Science+Business Media, New York, 2012.

      [3] M. Kot, Elements of Mathematical Biology, Cambridge University Press, United Kingdom, 2001.

      [4] J. D. Murray, Mathematical Biology I. An Introduction, Springer-Verlag, Berlin, 2002.

      [5] A. Okubo and S.A. Levin, Diffusion and Ecological Problems: Modern Perspectives, Springer, New York, 2001.

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  • How to Cite

    Ndam, J. (2015). Analysis of the long-time asymptotic behaviour of the solution of a two-dimensional reaction-diffusion equation. International Journal of Applied Mathematical Research, 4(2), 332-335. https://doi.org/10.14419/ijamr.v4i2.4426