An Application of Convolution Expansions to an Infinite System of Differential Equations

In the paper, we consider discrete version of the Tjon-Wu equation. We obtain proof of the existence and uniqueness of global nonnegative solutions of the Cauchy problem. Moreover, the behaviour of these solutions is described for a wide class of initial distributions. The main tool is the Wild expansion, properties of convolution iterates and convexing feature of summation.