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July/August 2017 Stable and unstable manifolds for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions
Roland Schnaubelt
Adv. Differential Equations 22(7/8): 541-592 (July/August 2017).

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.

Citation

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Roland Schnaubelt. "Stable and unstable manifolds for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions." Adv. Differential Equations 22 (7/8) 541 - 592, July/August 2017.

Information

Accepted: 1 October 2016; Published: July/August 2017
First available in Project Euclid: 4 May 2017

zbMATH: 1377.35169
MathSciNet: MR3646470

Subjects:
Primary: 335K61, 35B35, 35B40, 35K59, 5B65

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.22 • No. 7/8 • July/August 2017
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