Differential and Integral Equations
- Differential Integral Equations
- Volume 8, Number 4 (1995), 753-796.
Center manifolds for quasilinear reaction-diffusion systems
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.
Differential Integral Equations, Volume 8, Number 4 (1995), 753-796.
First available in Project Euclid: 20 May 2013
Permanent link to this document
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