Symmetry of Positive Solutions of Asymptotically Symmetric Parabolic Problems on $${{mathbb R}^N}$$ |
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Authors: | Juraj Földes |
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Affiliation: | 1.Department of Mathematics,Vanderbilt University,Nashville,USA |
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Abstract: | In this paper we investigate symmetry properties of positive solution of quasilinear parabolic problems in the whole space. As the main result, we prove that if the problem converges exponentially to a symmetric one, then the solution converges to the space of symmetric functions. We also show, that this result does not hold true, if the convergence is not exponential. |
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