Invariant regions and global existence of solutions for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients and nonhomogeneous boundary conditions.

Salem, Abdelmalek

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We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.