Modeling and analysis of reactive multi-component two-phase flows with mass transfer and phase transition -- the isothermal incompressible case
The authors discuss the isothermal incompressible multi-component two-phase flows with mass transfer, chemical reactions, and phase transition based on first principles. They prove that the resulting system is thermodynamically consistent in the sense that the available energy is a strict Lyapunov functional, and the equilibria are identified. They prove that the problem is well-posed in an \(L_p\)-setting, and generates a local semiflow in the proper state manifold. They prove that each non-degenerate equilibrium is dynamically stable in the natural state manifold. Finally, they prove that a solution, which doesn't develop singularities, exists globally and converges to an equilibrium in the state manifold. The paper is interesting and deep.
quasi-linear parabolic evolution equations
generalized principle of linearized stability
scientific article; zbMATH DE number 6710662
scientific article