摘要
研究了一类二阶双曲型微分方程 vxx-h( x,y) k( y) vyy+ a( x,y) vx+ b( x,y) vy+ c( x,y) v+ f ( x,y) =0的柯西问题解的存在性 .现在采用较为初等的方法 ,即通过构造积分方程的逼近解序列 ,把这个问题转化为一个积分方程组问题 ,然后再利用归纳法和迭代法 ,证明这类二阶双曲型微分方程在一定条件下的柯西问题有解且可导 。
Deals with the Cauchy problem for a hyperbolic equation of second order v xx -h(x,y)k(y)v yy +a(x,y)v x+b(x,y)v y+c(x,y)v+f(x,y)=0. The equation was made a breakthrough in form,and primary methods have been quoted.First,the problem was tramstorm into a system of integral equations through structuring a pressing alignment,and then prove that the problem has differentiable solution under some conditions by using the iteration method.The expression with integral equations is given.
出处
《河北师范大学学报（自然科学版）》
CAS
2001年第4期432-435,437,共5页
Journal of Hebei Normal University：Natural Science
基金
河北省自然科学基金资助项目 ( 19815 5 )
