Symmetrization and anti-symmetrization in parabolic equations
Analysis of PDEs
2016-04-29 v2
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.
Keywords
Cite
@article{arxiv.1604.03825,
title = {Symmetrization and anti-symmetrization in parabolic equations},
author = {Luca Rossi},
journal= {arXiv preprint arXiv:1604.03825},
year = {2016}
}