On a spectral problem for a system of differential equations of mixed type

This article explores the spectral characteristics of the differential operator generated by the boundary problem for linear systems of differential equations of mixed type. The simplest example of a classical system of equations that falls within the field of our consideration is the system of equations of mixed type:
$$D_tu_1-{\rm sign}D_xu_2-\varepsilon u_2=f_1, \quad D_tu_2+D_xu_1+\varepsilon u_1=f_2$$
Elliptic for $t>0$ and hyperbolic for $t<0$.