Linearized Stability of Equilibrium Solutions to the Quasi-Gasdynamic System of Equations

Linearized stability of equilibrium solutions at constant temperature to the quasi-gasdynamic (QGD) system of equations is studied. The QGD system of equations are considered for mass balance, momentum, and total energy. The QGD system in the cylinder with certain the boundary conditions are considered and stationary equilibrium solutions are introduced. The QGD system is linearized at the equilibrium solution by substitutions and discarding the second-order terms with respect to the perturbations and their derivatives. A function that is a weak solution of the initial-boundary value problem is found. The eigenvalue problem is found to have a solution for a countable set of eigenvalues of finite multiplicity and the solvability result for the eigenvalue problem is standard.