合肥工业大学学报(自然科学版)
閤肥工業大學學報(自然科學版)
합비공업대학학보(자연과학판)
JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY
2010年
4期
597-599
,共3页
解的爆破%广义超弹性杆方程%Cauchy问题
解的爆破%廣義超彈性桿方程%Cauchy問題
해적폭파%엄의초탄성간방정%Cauchy문제
blow-up of solution%generalized hyperelastic-rod equation%Cauchy problem
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.
非線性髮展方程的初邊值問題包括方程解的存在性、唯一性、穩定性、爆破性和正則性等,是非線性髮展方程的最基本問題之一.文章主要從特徵麯線的角度研究廣義超彈性桿方程Cauchy問題解的爆破條件,使得解在有限時間內爆破的條件取決于最小初始速度的梯度變化範圍以及初始值和廣義函數g(u)的有界性,即初值和有界函數g(u)在文中所指定條件下,廣義超彈性桿方程Cauchy問題會產生爆破現象.
비선성발전방정적초변치문제포괄방정해적존재성、유일성、은정성、폭파성화정칙성등,시비선성발전방정적최기본문제지일.문장주요종특정곡선적각도연구엄의초탄성간방정Cauchy문제해적폭파조건,사득해재유한시간내폭파적조건취결우최소초시속도적제도변화범위이급초시치화엄의함수g(u)적유계성,즉초치화유계함수g(u)재문중소지정조건하,엄의초탄성간방정Cauchy문제회산생폭파현상.
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.
