Differential and Integral Equations

Center manifolds for quasilinear reaction-diffusion systems

Gieri Simonett

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We consider strongly coupled quasilinear reaction-diffusion systems subject to nonlinear boundary conditions. Our aim is to develop a geometric theory for these types of equations. Such a theory is necessary in order to describe the dynamical behavior of solutions. In our main result we establish the existence and attractivity of center manifolds under suitable technical assumptions. The technical ingredients we need consist of the theory of strongly continuous analytic semigroups, maximal regularity, interpolation theory and evolution equations in extrapolation spaces.

Article information

Differential Integral Equations, Volume 8, Number 4 (1995), 753-796.

First available in Project Euclid: 20 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35K60: Nonlinear initial value problems for linear parabolic equations 58D25: Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]


Simonett, Gieri. Center manifolds for quasilinear reaction-diffusion systems. Differential Integral Equations 8 (1995), no. 4, 753--796. https://projecteuclid.org/euclid.die/1369055610

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