Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. Part II

Asymptotic stability by Lyapunov of the steady-state solution to the linear initial-boundary value problem which is formulated in the first part of this paper [A.M. Blokhin, D.L. Tkachev, L.O. Baldan, Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. Part I, J. Math. Anal. Appl. 331 (1) (2007) 408–423 (this issue)] proved under two conditions. The main of these conditions is that zeros of Lopatinsky determinant excluding η=0, s=0 lie in the left half-plane. The problem arises while providing grounds for replacing of thin transitional zones of strong gradients of basic flow parameters for viscous heat-conducting gas with surfaces of strong discontinuity.