Advances in Differential Equations

Stability of periodic solutions to parabolic problems with nonlinear boundary conditions

Lahcen Maniar and Roland Schnaubelt

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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

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

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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