Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions |
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Authors: | Yuri Latushkin Jan Prüss Roland Schnaubelt |
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Affiliation: | 1. Department of Mathematics, University of Missouri–Columbia, Columbia, MO, 65211, USA 2. FB Mathematik und Informatik, Martin–Luther–Universit?t, 06099, Halle, Germany
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Abstract: | We investigate quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains in the setting of Sobolev–Slobodetskii spaces. We establish local wellposedness and study the time and space regularity of the solutions. Our main results concern the asymptotic behavior of the solutions in the vicinity of a hyperbolic equilibrium. In particular, the local stable and unstable manifolds are constructed. Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday |
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Keywords: | 35B38 35B40 35B68 35K35 35K50 35K57 |
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