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

被引：1
作者：
Asai, Taisei [1 ]
Tanaka, Kazuaki [2 ]
Oishi, Shin'ichi [3 ]
机构：
[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
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 399卷
关键词：
Henon equation; Numerical verification; Symmetry-breaking bifurcation; Elliptic boundary value problem; MULTIPLE POSITIVE SOLUTIONS; BIFURCATION METHOD; EIGENVALUE; SYMMETRY;
D O I：
10.1016/j.cam.2021.113708
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页数：13
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