Numerical verification for asymmetric solutions of the H\'enon equation on bounded domains
Abstract
The H\'enon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We discuss a numerical verification method for proving the existence of solutions of the H\'enon equation on a bounded domain. By applying the method to a line-segment domain and a square domain, we numerically prove the existence of solutions of the H\'enon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of undiscovered solutions with three peaks on the square domain.
Keywords
Cite
@article{arxiv.2002.02160,
title = {Numerical verification for asymmetric solutions of the H\'enon equation on bounded domains},
author = {Taisei Asai and Kazuaki Tanaka and Shin'ichi Oishi},
journal= {arXiv preprint arXiv:2002.02160},
year = {2021}
}
Comments
20 pages, 2 figures