Advances in Differential Equations

Nonnegative global solutions to a class of strongly coupled reaction-diffusion systems

Hiroki Hoshino

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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.

Article information

Adv. Differential Equations, Volume 5, Number 7-9 (2000), 801-832.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35D05 35K55: Nonlinear parabolic equations


Hoshino, Hiroki. Nonnegative global solutions to a class of strongly coupled reaction-diffusion systems. Adv. Differential Equations 5 (2000), no. 7-9, 801--832.

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