转移方程在焦散面近旁的解

THE SOLUTION OF TRANSPORT EQUATION NEAR A CAUSTIC

本文得出:当不恒为零的初始数据给在焦散面上时,转移方程(4)的Cauchy问题无解,指出方程(4)的解在焦散面上具有奇异性,并在焦散面近旁给出转移方程(4″)的一种解法.

In this paper it is found that the Cauchy problem of transpose equation 2▽φ·▽g + g△φ = 0 does not have solution when a nonvanishing initial value is given on a caustic, and that solutions of the transpose equation possess singularity at a caustic.We give a method to find out the solutions of the improved transpose equation （ cf.[1]）. 2△φ±·▽g±+ [△φ±?1/2ρ-1/2（▽ρ）2]g±=0 mear a caustic.