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Creators/Authors contains: "Weth, Tobias"

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  1. ; ; (, Journal of Dynamics and Differential Equations)
    We study the asymptotic (in time) behavior of positive and sign-changing solutions to nonlin- ear parabolic problems in the whole space or in the exterior of a ball with Dirichlet boundary conditions. We show that, under suitable regularity and stability assumptions, solutions are asymptotically (in time) foliated Schwarz symmetric, i.e., all elements in the associated omega-limit set are axially symmetric with respect to a common axis passing through the origin and are nonincreasing in the polar angle. We also obtain symmetry results for solu- tions of Hénon-type problems, for equilibria (i.e. for solutions of the corresponding elliptic problem), and for time periodic solutions. 
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