Existence and Nonlinear Stability of Stationary Solutions to the Full Two-Phase Flow Model in a Half Line

TL;DR

This paper investigates the existence, uniqueness, and nonlinear stability of stationary solutions to the full two-phase flow model in a half line, using center manifold theory and analyzing small perturbations.

Contribution

It provides the first rigorous proof of stationary solution existence and stability for the full two-phase flow model in a half line.

Findings

Existence and uniqueness of stationary solutions established.

Nonlinear stability of solutions proven for small perturbations.

Application of center manifold theory to two-phase flow models.

Abstract

The inflow problem for the full two-phase model in a half line is investigated in this paper. The existence and uniqueness of the stationary solution is shown by applications of center manifold theory, and its nonlinear stablility of the stationary solution is established for the small perturbation.