English

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}
}