Quasilinear Parabolic Systems with Nonlinear Boundary Conditions
نویسندگان
چکیده
منابع مشابه
Center Manifolds and Dynamics near Equilibria of Quasilinear Parabolic Systems with Fully Nonlinear Boundary Conditions
We study quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains. Our main results concern the asymptotic behavior of the solutions in the vicinity of an equilibrium. The local center, center–stable, and center–unstable manifolds are constructed and their dynamical properties are established using nonautonomous cuto...
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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 p...
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We construct and investigate local invariant manifolds for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions and study their attractivity properties. In a companion paper we have developed the corresponding solution theory. Examples for the class of systems considered are reaction–diffusion systems or phase field models with dynamical boundary co...
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متن کاملParabolic Systems with Coupled Boundary Conditions
We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space W . The system is equipped with a general class of coupled boundary conditions of the form f|∂Ω ∈ Y and ∂f ∂ν ∈ Y⊥, where Y is a closed subspace of L(∂Ω;W ). We discuss well-posedness and further qualitative properties, systema...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2000
ISSN: 0022-0396
DOI: 10.1006/jdeq.2000.3784