广义超弹性杆方程解的爆破

非线性发展方程的初边值问题包括方程解的存在性、唯一性、稳定性、爆破性和正则性等,是非线性发展方程的最基本问题之一。文章主要从特征曲线的角度研究广义超弹性杆方程Cauchy问题解的爆破条件,使得解在有限时间内爆破的条件取决于最小初始速度的梯度变化范围以及初始值和广义函数g(u)的有界性,即初值和有界函数g(u)在文中所指定条件下,广义超弹性杆方程Cauchy问题会产生爆破现象。

Blow-up of solution for generalized hyperelastic-rod equation

The issue of initial boundary value is one of basic issues of nonlinear evolution equations.It includes the existence,uniqueness,stability,blow-up and regularity of the solution.In this paper,the condition of the blow-up of the solution for Cauchy problem in generalized hyperelastic-rod equation is studied from the angle of characteristic curve.The blow-up of solution in finite time lies on the gradient changing scope of minimal initial velocity and the initial value and the boundedness of generalized function g(u).That is,when the initial value and the bounded generalized function g(u) satisfy the conditions specified in the paper,Cauchy problem in generalized hyperelastic-rod equation causesblow-up.