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Symmetrization and anti-symmetrization in parabolic equations

Author: Luca Rossi
Journal: Proc. Amer. Math. Soc. 145 (2017), 2527-2537
MSC (2010): Primary 35K10, 35B06; Secondary 35B40
Published electronically: December 9, 2016
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Abstract: We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones (1983) a quantitative estimate of how far the level sets of solutions are from being spherical. Next, using this property, we derive a criterion providing solutions whose level sets do not converge to spheres for a class of equations including linear equations and Fisher-KPP reaction-diffusion equations.

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Additional Information

Luca Rossi
Affiliation: CNRS, Ecole des Hautes Etudes en Sciences Sociales, PSL Research University, Centre d’Analyse et Mathématiques Sociales, 190-198 avenue de France F-75244 Paris Cedex 13, France

Received by editor(s): April 13, 2016
Received by editor(s) in revised form: July 20, 2016
Published electronically: December 9, 2016
Communicated by: Yingfei Yi
Article copyright: © Copyright 2016 American Mathematical Society

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