Differential and Integral Equations
- Differential Integral Equations
- Volume 9, Number 4 (1996), 761-778.
On the convergence properties of global solutions for some reaction-diffusion systems under Neumann boundary conditions
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.
Differential Integral Equations, Volume 9, Number 4 (1996), 761-778.
First available in Project Euclid: 7 May 2013
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Hoshino, Hiroki. On the convergence properties of global solutions for some reaction-diffusion systems under Neumann boundary conditions. Differential Integral Equations 9 (1996), no. 4, 761--778. https://projecteuclid.org/euclid.die/1367969886