Stability of the one-dimensional motions of a viscous gas with a linear dependence of the velocity on the coordinates

The stability of a new solution of the equations of one-dimensional gas dynamics is investigated. This solution is a generalization of the solutions of Sedov /1, 2/ to the case of a viscous, thermally conducting ideal gas with an exponential dependence of the coefficient of viscosity and thermal conductivity on temperature. The linearized equations for small perturbations (the effects of thermal conductivity are not allowed for in the equations for the perturbations), which contain functions of time and the radial coordinate in the coefficients, can be solved by separation of the variables. The conditions under which instability arises are determined from an analysis of the time parts of the solutions. The stability of the solutions /1/ has been considered in /3-5/.