Symmetrization and anti-symmetrization in parabolic equations

2016/04/13 by Rossi, Luca
#35B06 #35B40 #35K10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.03825

Abstract

We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones 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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