## Differential and Integral Equations

### On the convergence properties of global solutions for some reaction-diffusion systems under Neumann boundary conditions

Hiroki Hoshino

#### Abstract

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.

#### Article information

Source
Differential Integral Equations, Volume 9, Number 4 (1996), 761-778.

Dates
First available in Project Euclid: 7 May 2013