一类模拟悬索桥的von Kármán方程的解的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1112-1121.

一类模拟悬索桥的von Kármán方程的解的存在性

王永达()

河北大学数学与信息科学学院, 河北保定 071002

收稿日期:2021-03-22 出版日期:2022-08-26 发布日期:2022-08-08
作者简介:王永达, E-mail: wangyongda@hbu.cn
基金资助:
河北省自然科学基金(A2019201106);河北大学高层次人才引进项目(521000981097);国家自然科学基金(11771115)

Existence Results for von Kármán Equations Modeling Suspension Bridges

Yongda Wang()

College of Mathematics and Information Science, Hebei University, Hebei Baoding 071002

Received:2021-03-22 Online:2022-08-26 Published:2022-08-08
Supported by:
the NSF of Hebei Province(A2019201106);the Advanced Talents Incubation Program of Hebei University(521000981097);the NSFC(11771115)

摘要/Abstract

摘要：

该文研究了一类具有部分自由边界的非线性von Kármán方程, 它可以看作是发生大形变悬索桥的数学模型.方程中引入了产生非局部效应的屈曲载荷.通过分析相应能量泛函的临界点, 我们得到了方程的解的唯一性和多解性.

关键词: von Kármán方程, 悬索桥, 自由边界, 屈曲载荷

Abstract:

A nonlinear von Kármán equation with partial free boundary is considered. The equation is viewed as a mathematical model for suspension bridges with large deformation. The buckling loads, which carry a nonlocal effect into the model, are introduced. Uniqueness and multiplicity results are obtained by analyzing the critical points of the energy functionals.

Key words: von Kármán equation, Suspension bridge, Free boundary, Buckling loads

中图分类号:

O174.56

王永达. 一类模拟悬索桥的von Kármán方程的解的存在性[J]. 数学物理学报, 2022, 42(4): 1112-1121.

Yongda Wang. Existence Results for von Kármán Equations Modeling Suspension Bridges[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1112-1121.

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