Differential and Integral Equations

Center manifolds for quasilinear reaction-diffusion systems

Gieri Simonett

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Abstract

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

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

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369055610

Mathematical Reviews number (MathSciNet)
MR1306591

Zentralblatt MATH identifier
0815.35054

Subjects
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]

Citation

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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