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2000 Nonnegative global solutions to a class of strongly coupled reaction-diffusion systems
Hiroki Hoshino
Adv. Differential Equations 5(7-9): 801-832 (2000). DOI: 10.57262/ade/1356651288


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.


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Hiroki Hoshino. "Nonnegative global solutions to a class of strongly coupled reaction-diffusion systems." Adv. Differential Equations 5 (7-9) 801 - 832, 2000.


Published: 2000
First available in Project Euclid: 27 December 2012

zbMATH: 0987.35076
MathSciNet: MR1776342
Digital Object Identifier: 10.57262/ade/1356651288

Primary: 35K57
Secondary: 35B40 , 35D05 , 35K55

Rights: Copyright © 2000 Khayyam Publishing, Inc.


Vol.5 • No. 7-9 • 2000
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