×

Center manifolds for quasilinear reaction-diffusion systems. (English) Zbl 0815.35054

Summary: 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.

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
47D06 One-parameter semigroups and linear evolution equations