In this paper the new procedure for a construction of an approximated solution to initial data problem for one-dimensional pressureless gas dynamics system is introduced. The procedure is based on solving the Riemann problems and tracking singular wave interactions. For that system the new problem with initial data containing Dirac delta function is solved whenever two waves interact. Use of the shadow waves as singular solutions to such problems enables us to easily solve the interaction problems. That permits us to make a simple extension of the well known Wave Front Tracking algorithm. A non-standard part of the new algorithm is dealing with delta functions as a part of a solution. In the final part of the paper we show that the approximated solution has a subsequence converging to a signed Radon measure.

本文介绍了一种为一维无压气体动力学系统构造初始数据问题的近似解的新方法。该过程基于解决黎曼问题并跟踪奇异波相互作用。对于该系统，每当两个波相互作用时，就解决了包含Dirac delta函数的初始数据的新问题。使用阴影波作为此类问题的奇异解使我们能够轻松解决相互作用问题。这使我们可以对众所周知的波前跟踪算法进行简单扩展。新算法的非标准部分是将增量函数作为解决方案的一部分。在本文的最后部分，我们证明了近似解具有一个收敛于有符号Radon测度的子序列。