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