一类可扩充杆横截挠度方程的Cauchy问题

数学物理学报 ›› 2003, Vol. 23 ›› Issue (6): 704-710.

一类可扩充杆横截挠度方程的Cauchy问题

张全举

西安建筑科技大学理学院西安 710055

出版日期:2003-12-25 发布日期:2003-12-25
基金资助:
陕西省教育厅专项基金资助（01JK201）项目

The Cauchy Problems of a class of Equations |for the Tension of Extensible Beam

ZHANG Quan-Ju

西安建筑科技大学理学院西安 710055

Online:2003-12-25 Published:2003-12-25
Supported by:
陕西省教育厅专项基金资助（01JK201）项目

摘要/Abstract

摘要：

讨论一类刻划可扩充杆横截挠度的非线性双曲型方程utt+A2u+M(x，‖A1/2 u ‖22)Au=0，这里A=-Δ+I，x∈R\+n，Cauchy问题解的存在唯一性，给出了此方程有唯一局部解的存在定理.文章所给出的结果的适用性要远大于已有的与此问题相关的结论，对此方程非线性项的假设要比一般的多.事实上，文章的结果是在打破了以前的所有限制而得到的.
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关键词: 横截挠度;双曲型方程;Cauchy问题;存在唯一性

Abstract:

This paper deals with the hyperbolic equation in the form of utt+A2u+M(x，‖A1/2u‖22)Au=0，which comes from the mathematical description of the tension of a extensible bea m, and the existence and uniqueness of Cauchy problems for this equation are pre sented here. An existence and uniqueness theorem of local solvability is proven for this equation, and compared with the existing results, the author's conditio ns restri cted to the nonlinear term of this equation are much general. In fact, the resul ts given here are obtained by breaking all the former restrictions on the nonlin ear term.

Key words: Tension of a extensible beam, Hyperbolic equation, Cauchy problems, Existence and uniqueness theorem

中图分类号:

35L70

张全举. 一类可扩充杆横截挠度方程的Cauchy问题[J]. 数学物理学报, 2003, 23(6): 704-710.

ZHANG Quan-Ju. The Cauchy Problems of a class of Equations |for the Tension of Extensible Beam[J]. Acta mathematica scientia,Series A, 2003, 23(6): 704-710.