摘要
Asgeirsson中量定理表明超双曲型方程的Cauchy问题一般是不适定的。利用非齐次超双曲型方程的中量定理的结果和积分、微分的性质与关系 ,得到了高阶非齐次方程 (Δ2 x-Δ2 y)u =f(x ,y)解的中量满足广义轴对称位势非齐次方程 。
The famous Asgeirsson mean value theorem makes Cauchy problems in the ultra-hyperbolic equations poor posed. So it is important to advance Asgeirsson mean value theorem. By using the properties of mean value theorem for variable coefficient equations and the relations between derivation and integration, a mean value theorem for the higher order equation with a variable coefficient is gained. Its converse theorem is proved, which makes the discussion on continuation of the solutions and well posed problem possible.
出处
《石油大学学报（自然科学版）》
CSCD
北大核心
2001年第5期109-110,112,共3页
Journal of the University of Petroleum,China(Edition of Natural Science)
