一维Chaplygin气体欧拉方程组中波的相互作用

研究一维Chaplygin气体欧拉方程组中波的相互作用.方程组的波包含接触间断和在密度变量以及内能变量上同时具有狄拉克函数的狄拉克激波.根据这些波的不同组合,问题被分成了7种情形.通过详细地构造每种情形的整体解,获得了各种波相互作用的完整结果.特别地,对于一类初值,两个接触间断相互作用后,产生了一个狄拉克激波;然而,对于另外一类初值,一个狄拉克激波与一个接触间断相互作用后,狄拉克激波消失.这些都是波相互作用中非常特别的现象.

Interaction of Waves in One-Dimensional Compressible Euler Equations for a Chaplygin Gas

The interaction of waves in one-dimensional compressible Euler equations for a Chaplygin gas is considered.The waves of this system consist of contact discontinuity and delta shock wave in which both density and internal energy contain Dirac delta function simultaneously.According to the different combinations of these waves,this problem is divided into 7 cases.By constructing the global solution to each case in detail,one obtains a variety of structures for the interaction of these waves.It is found that,for one kind of initial data,a delta shock wave develops after the interaction between two contact discontinuities,and that,for anther kind of initial data,a delta shock wave vanishes after its interaction with a contact discontinuity.These axe interesting phenomena in the interaction of waves.