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Symmetrization and anti-symmetrization in parabolic equations

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.

preprint2016arXivOpen access
Luca Rossi
math.AP
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Luca Rossi

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