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

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    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.


  • Keywords


    Reaction-diffusion equation; Energy function; Poincare inequality; Reflecting boundary conditions.

  • References


      [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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Article ID: 4426
 
DOI: 10.14419/ijamr.v4i2.4426




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