Stability of periodic solutions to parabolic problems with nonlinear boundary conditions

Maniar, Lahcen
Schnaubelt, Roland

facul_11; 18

Date: 23. 12. 2009
Abstract:
We investigate non-autonomous quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions. We establish local wellposedness and
study the time and space regularity of the solutions. Our main results give principles of linearized (orbital) stability and instability for solutions in the vicinity of a periodic solution. Our approach relies on a detailed study of regularity properties of the linearized nonautonomous problem and its evolution family.

Primary MSC: 35B40 Asymptotic behavior of solutions , 35K35 Initial-boundary value problems for higher-order parabolic equations , 35K59 Quasilinear parabolic equations
Keywords: Orbital stability, asymptotic phase, maximal regularity, linearization, monodromy operator, exponential dichotomy, extrapolation, Acquistapace-Terreni conditions