四阶非齐次方程(Δ_x^2-Δ_y^2)u=f(x,y)解的中量定理及其逆定理  

MEAN VALUE THEOREMS AND A CONVERSE THEOREM FOR A CLASS OF HIGHER ORDER EQUATION WITH A VARIABLE COEFFICIENT

作　　者：同小军[1] 

机构地区：[1]石油大学应用数学系,山东东营257061

出　　处：《石油大学学报（自然科学版）》2001年第5期109-110,112,共3页Journal of the University of Petroleum,China(Edition of Natural Science)

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.

关 键 词：Asgeirsson中量定理 广义轴对称位势方程 Green公式 四阶非齐次方程 超双曲型方程 

分 类 号：O175.27[理学—数学]