Advances in Differential Equations

Stable and unstable manifolds for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions

Roland Schnaubelt

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Abstract

We develop a wellposedness and regularity theory for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions. Moreover, we construct and investigate stable and unstable local invariant manifolds near a given equilibrium. In a companion paper, we treat center, center-stable and center-unstable manifolds for such problems and investigate their stability properties. This theory applies e.g. to reaction-diffusion systems with dynamical boundary conditions and to the two-phase Stefan problem with surface tension.

Article information

Source
Adv. Differential Equations Volume 22, Number 7/8 (2017), 541-592.

Dates
Accepted: October 2016
First available in Project Euclid: 4 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1493863421

Zentralblatt MATH identifier
1377.35169

Subjects
Primary: 35B35: Stability 35B40: Asymptotic behavior of solutions 5B65 35K59: Quasilinear parabolic equations 335K61

Citation

Schnaubelt, Roland. Stable and unstable manifolds for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions. Adv. Differential Equations 22 (2017), no. 7/8, 541--592. https://projecteuclid.org/euclid.ade/1493863421


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