Global Attractors for Semilinear Parabolic Problems Involving X-Elliptic Operators

Stefanie Sonner

Abstract


We consider semilinear parabolic equations involving an operator that is X-elliptic with respect to a family of vector fields X with suitable properties. The vector fields determine the natural functional setting associated to the problem and the admissible growth of the non-linearity. We prove the global existence of solutions and characterize their longtime behavior. In particular, we show the existence and finite fractal dimension of the global attractor of the generated semigroup and the convergence of solutions to an equilibrium solution when time tends to infinity.

Keywords


Semilinear degenerate parabolic equations; global attractors; sub-elliptic operators

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References


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DOI: 10.6092/issn.2240-2829/5889

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Copyright (c) 2015 Stefanie Sonner

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ISSN 2240-2829
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