Advances in Differential Equations
- Adv. Differential Equations
- Volume 5, Number 7-9 (2000), 801-832.
Nonnegative global solutions to a class of strongly coupled reaction-diffusion systems
A class of strongly coupled reaction-diffusion systems is studied. First, under some conditions, it is shown that a nonnegative solution exists globally in time. After that, asymptotic behavior of the nonnegative global solution is considered. Especially, when the solution uniformly converges to a steady state with a polynomial rate as time goes to infinity, large-time approximation of the solution is investigated. By the energy method and analytic semigroup theory, it is proved that a global solution for the corresponding system of ordinary differential equations has the role of an asymptotic solution for the reaction-diffusion system and that the spatial average of the global solution to the reaction-diffusion system gives an asymptotic description.
Adv. Differential Equations, Volume 5, Number 7-9 (2000), 801-832.
First available in Project Euclid: 27 December 2012
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Hoshino, Hiroki. Nonnegative global solutions to a class of strongly coupled reaction-diffusion systems. Adv. Differential Equations 5 (2000), no. 7-9, 801--832. https://projecteuclid.org/euclid.ade/1356651288