对简单压缩波定性理论的质疑

Raising Doubt About the Qualitative Theory of Simple Compression Wave

R.Courant和Landau等学者曾定性地断言,对于简单压缩波其特征线会相互相交,因而会使解出现多值性,由此产生了弱解理论。文章通过求一个具体问题的严格解析解,证明了上述断言纯属主观臆断,另外证明了特征线的包络就是间断面(或激波)运动的迹线,使弱解理论面临了困难。

Famous scholars R. Courant and Landau qualitatively affirmed that for simple compression wave the characteristic lines would intersect each other so that many-valuedness would happen and the theory of weak solution was invented. In t.this paper the exact analytical solution of a concrete problem has been found and it has been proven that the above affirmation is only a subjective assumption. In addition it has been also proven that the envelope of characteristic lines is surely the trace of discontinuing motion (or shock wave) . So the theory of weak solution has faced difficulty.