二阶退化双曲型方程的第二类广义Darboux问题

Generalized Darboux's Second Problem for Degenerate Hyperbolic Equations

A.V.Bitsadze在文[1]中提出和研究了二阶一致线性双曲型方程uxx-uyy+aux+by+cu+d=0(A)的第一类和第二类Darboux问题.本文的目的是讨论二阶退化双曲型方程第二类广义Darboux问题和斜微商问题解的表示式,并证明这些问题解的存在唯一性。本文使用不同于[1]中的方法,但类似于[1]中的方程(A),根据本文中的结果,我们可以解决广义Chaplygin方程在一般区域上的Frankl问题.

In [l], A.V.Bitsadze put forward and discussed Darboux＇s first and second problems for the unear hyperbolicequation uxx-Uyy＋aux＋by＋cu＋d=0 without parabolic degenerate line in a closed domain D. The present paper dealt with some boundary value problems for the degenerate hyperbolic equations of second order. The representations of solutions for Darboux＇s second problem and oblique derivative problem in general domains were given, and the existence and uniqueness of solutions for the problems were proved. The method in this paper is different from that in [ 1 ] and simpler than that for the equation （A） in [ 1 ], by the result in this paper, the Frankl problem can be solved of generalized Chaplygin equations in general domains.