On the asymptotic shape of solutions to Neumann problems for non-cooperative parabolic systems
Analysis of PDEs
2023-07-19 v3
Abstract
We consider a class of nonautonomous parabolic competition-diffusion systems on bounded radial domains under Neumann boundary conditions. We show that, if the initial profiles satisfy a reflection inequality with respect to a hyperplane, then global positive solutions are asymptotically (in time) foliated Schwarz symmetric with respect to antipodal points. Additionally, a related result for (positive and sign changing solutions) of a scalar equation with Neumann boundary conditions is given. The asymptotic shape of solutions to cooperative systems is also discussed.
Keywords
Cite
@article{arxiv.1403.1133,
title = {On the asymptotic shape of solutions to Neumann problems for non-cooperative parabolic systems},
author = {Alberto Saldaña and Tobias Weth},
journal= {arXiv preprint arXiv:1403.1133},
year = {2023}
}
Comments
30 pages. Revised version