# Numerical verification for asymmetric solutions of the Hénon equation on bounded domains

Taisei Asai*, Kazuaki Tanaka, Shin'ichi Oishi

*この研究の対応する著者

## 抄録

The Hénon 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 Hénon 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 Hénon 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.

本文言語 English 113708 Journal of Computational and Applied Mathematics 399 https://doi.org/10.1016/j.cam.2021.113708 Published - 2022 1月 1

• 計算数学
• 応用数学

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