Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line (Communications in Mathematical Research, 2020)
The outflow problem for the viscous two-phase flow model in a halfline is investigated in the present paper. The existence and uniqueness of thestationary solution is shown for both supersonic state and sonic state at spatialfar field, and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decayrate for supersonic flow or the algebraic time decay rate for sonic flow.
Keywords: Two-phase flow; outflow problem; stationary solution; nonlinear stability.