Mat. Sb. (N.S.), 1950 Volume 27(69), Number 2,Pages 319–323(Mi sm5921)
An example of nonuniqueness of solution of Cauchy's problem for a system of the form $\displaystyle\frac{\partial u_i}{\partial t}=\sum_jA_{ij}\frac{\partial u_j}{\partial x}+\sum_jB_{ij}u_j+f_i$ $(i,j=1,2)$