Differential and Integral Equations

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

Hiroki Hoshino

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.die/1367969886

Mathematical Reviews number (MathSciNet)
MR1401436

Zentralblatt MATH identifier
0852.35023

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 47N20: Applications to differential and integral equations 92D30: Epidemiology

Citation

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


Export citation