Advances in Differential Equations

Stability of periodic solutions to parabolic problems with nonlinear boundary conditions

Lahcen Maniar and Roland Schnaubelt

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Abstract

We investigate nonautonomous 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.

Article information

Source
Adv. Differential Equations Volume 17, Number 5/6 (2012), 557-604.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703079

Mathematical Reviews number (MathSciNet)
MR2951940

Zentralblatt MATH identifier
1260.35008

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35K35: Initial-boundary value problems for higher-order parabolic equations 35K59: Quasilinear parabolic equations

Citation

Maniar, Lahcen; Schnaubelt, Roland. Stability of periodic solutions to parabolic problems with nonlinear boundary conditions. Adv. Differential Equations 17 (2012), no. 5/6, 557--604. https://projecteuclid.org/euclid.ade/1355703079.


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