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arXiv · 1604.03825

Symmetrization and anti-symmetrization in parabolic equations

Luca Rossi
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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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Luca Rossi. 2016-04-28. Symmetrization and anti-symmetrization in parabolic equations. https://arxiv.org/abs/1604.03825

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