【摘要】 本文就形如utt =a2 (utt+2xux)的Cauchy问题进行了讨论 ,得到其相容性条件和古典解的存在性定理 ,进而对于更一般的一类形如autt+2butt+cutt+2x(aux+bux) =0 (a、b、c是常量 ,且b2 -ac>0 )的方程得到类似结果更多还原

【Abstract】 It is discussed here with the cauchy problem for a selond-order hyperbolic equation: u tt =a 2(u tt +2xu x) The paper gets the necessary condition (the consistency condition)for the txistence of the classical colution,and the existence theorem.Similar results are obtained,too,for a more extensive equation: au tt +2bu tt +cu tt +2x(au x+bu x)=0更多还原