一类非线性发展方程组的解的定性性质  

Qualitative Properties of Solutions of a Class of Nonlinear Evolution Equations

作　　者：袁学刚[1] 孙国寿 张文正[3] 

机构地区：[1]大连民族学院理学院,辽宁大连116605 [2]山东德信建设集团股份有限公司,山东烟台264005 [3]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《大连民族学院学报》2008年第1期47-50,共4页Journal of Dalian Nationalities University

基　　金：国家自然科学基金资助项目(10626045)

摘　　要：将一类非线性发展方程组的初边值问题约化为一个二阶非线性常微分方程。该微分方程可以描述在表面突加的拉伸死载荷作用下,不可压缩的广义Valanis-Landel材料组成的超弹性球体内部空穴的生成和运动。分别从方程的平衡解的静态分岔、解的存在条件以及解的动力学性质3个方面讨论了各个参数对微分方程的解的定性性质的影响。证明了空穴生成后随时间的运动是非线性的周期振动,并给出了数值模拟。A class of nonlinear evolution equations with initial - boundary conditions is reduced to a second - order ordinary differential equation, which may describe the formation and motion of cavity in the hyper - elastic sphere composed of a class of generalized Valanis - Landel materials and the sphere is subjected to a suddenly applied surface tensile constant load. The effect of each parameter on the solutions of the differential equation is discussed in details by studying the static bifurcation of the equilibrium solutions, the existent conditions of the nonzero solutions and the dynamical behaviors of the solutions of the equation. It is proved that the motion of the formed cavity presents a nonlinear periodic oscillation. Some numerical simulations are given.

关 键 词：非线性发展方程 静态分岔 临界载荷 非线性周期振动 

分 类 号：O175[理学—数学] O343[理学—基础数学]