In this article, we study certain p-adic master equations which describe the dynamics of a large class of complex systems such as glasses, macromolecules and proteins. These equations are naturally associated to certain non-archimedean pseudo-differential operators whose symbols are connected via Fourier transform with radial probability density functions defined on the p-adic numbers. We show that the fundamental solutions of these equations are probability measures and determine a convolution semigroup on the p-adic numbers. Also, we show that the classical solution of this equations preserves the mass and satisfies the comparison principle. Moreover, we study some strong Markov processes corresponding to radial probability density functions of linear and logarithmic type.

在本文中，我们研究某些p -adic主方程，这些方程描述了诸如玻璃，大分子和蛋白质之类的一大类复杂系统的动力学。这些方程自然地与某些非阿基米德伪微分算子相关，其符号通过傅立叶变换与在p -adic数上定义的径向概率密度函数相连。我们证明了这些方程的基本解是概率测度并确定了p上的卷积半群-adic数字。同样，我们证明了该方程的经典解保留了质量并满足了比较原理。此外，我们研究了一些与线性和对数类型的径向概率密度函数相对应的强大马尔可夫过程。