无压气体模型的阴影波跟踪方法和初始数据问题
Shadow wave tracking procedure and initial data problem for pressureless gas model
摘要：
本文介绍了构造一维无压气体动力学方程组初值问题近似解的新方法。该程序是基于解决黎曼问题和跟踪奇异波相互作用。对于该系统，当两波相互作用时，初始数据包含Dirac δ函数的新问题得到了解决。利用阴影波作为这类问题的奇异解，使我们能够很容易地解决相互作用问题。这使得我们能够对著名的波前跟踪算法进行单扩张。新算法的一个非标准部分是将delta函数作为解决方案的一部分来处理。在本文的最后一部分，我们证明了近似解有一个子序列收敛到一个有符号的Radon测度。
英文摘要：
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.
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