We are concerned with the asymptotic behavior of global solutions for a class of reaction-diffusion systems under homogeneous Neumann boundary conditions. An example of the system which we consider in this paper is what we call a diffusive epidemic model. After we show that every global solution uniformly converges to the corresponding constant function as $t \to \infty$, we investigate the rate of this convergence. We can obtain it with use of $L^p$-estimates, integral equations via analytic semigroups, fractional powers of operators and some imbedding relations.
Hiroki Hoshino. "On the convergence properties of global solutions for some reaction-diffusion systems under Neumann boundary conditions." Differential Integral Equations 9 (4) 761 - 778, 1996. https://doi.org/10.57262/die/1367969886