The origin of the ultrahigh energy cosmic ray remains being a mystery. However, a considerable progress has been made in the past few years due to the good quality data recorded by current cosmic ray observatories. One of the recent achievements is obtaining firm observational evidence about the extragalactic origin of the most energetic cosmic rays by the Pierre Auger observatory. On the other hand, it is believed that there is a non-null turbulent magnetic field that fills the intergalactic medium. Therefore, the presence of the intergalactic magnetic field can play an important role on the propagation of the ultrahigh energy cosmic rays through the Universe, which in principle can be relevant to interpret the experimental data. In this work we present a system of partial differential equations that describes the propagation of the ultrahigh energy cosmic rays through the Universe, in the presence of a turbulent intergalactic magnetic field, that includes the diffusive and the ballistic regime of propagation and also the transition between them. Also, as an example of application, the system of equations is solved numerically in a simplified physical situation.

超高能宇宙线的起源仍然是个谜。然而，由于目前的宇宙线天文台记录的高质量数据，在过去几年中取得了相当大的进展。最近的成就之一是通过皮埃尔·奥格天文台获得了关于最高能量宇宙射线的河外起源的可靠观测证据。另一方面，人们相信存在充满星系际介质的非零湍流磁场。因此，星系际磁场的存在可以对超高能宇宙射线在宇宙中的传播发挥重要作用，这在原则上可以与实验数据的解释相关。在这项工作中，我们提出了一个偏微分方程系统，该系统描述了超高能宇宙射线在存在湍流星系间磁场的情况下在宇宙中的传播，其中包括传播的扩散和弹道传播状态以及两者之间的过渡他们。此外，作为应用示例，方程组在简化的物理情况下进行数值求解。