Self-similar and numerical solutions of MHD-equations with non-linear bulk sources and sinks

The influence of non-linear bulk sources and sinks of mass and energy upon non-stationary flow of gas in a magnetic field is studied. The qualitative analysis is carried out with the aid of self-similar solutions. Different models of sources and sinks (when either energy or enthalpy is carried away) are used. The dynamics of compressing and heating plasma in the $\theta$-pinch is investigated, when butt-end losses are taken into account. Qualitative regularities of the process are established.