Numerical verification for asymmetric solutions of the Henon equation on bounded domains

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:399

Article

Asai, Taisei¹  Tanaka, Kazuaki²  Oishi, Shin'ichi³ 

[1] Waseda Univ, Grad Sch Fundamental Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

[2] Waseda Univ, Inst Math Sci, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

[3] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

关键词: Henon equation;    Numerical verification;    Symmetry-breaking bifurcation;    Elliptic boundary value problem;   

DOI  :  10.1016/j.cam.2021.113708

来源: Elsevier

【 摘 要 】

The Henon 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 Henon 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 Henon 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. (C) 2021 The Authors. Published by Elsevier B.V.

【 授权许可】

Free