We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones (1983) 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.
Symmetrization and anti-symmetrization in parabolic equations / Rossi, L.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 145:6(2017), pp. 2527-2537. [10.1090/proc/13391]
Symmetrization and anti-symmetrization in parabolic equations
Rossi L.
2017
Abstract
We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones (1983) 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.| File | Dimensione | Formato | |
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