In this thesis we study the liquid-vapor phase transition modeled by Van Der Waals equation. This system is elliptic in some regions and hyperbolic in other regions. From [1] we know that the difficulty caused by the instability of solutions lying in the unstable elliptic region can be overcome by adding viscosity terms....[ Read more ]

In this thesis we study the liquid-vapor phase transition modeled by Van Der Waals equation. This system is elliptic in some regions and hyperbolic in other regions. From [1] we know that the difficulty caused by the instability of solutions lying in the unstable elliptic region can be overcome by adding viscosity terms.

We have done extensive numerical simulations for the Van Der Waals system for both one and two dimensional cases. For one dimensional system the boundary condition of temperature and the body force will both influence the behavior of system after a long period of time. The phenomena of two dimensional system are more interesting. The system will approach to two kinds of asymptotic states. One is trivial because the behavior of the system is uniform in some specific direction. We can consider it to be a degenerated one dimensional solution. Another one is a symmetric state of form ρ=ρ(γ), μ=φ(γ)cosθ and υ=φ(γ)sinθ. Existence of such solution is also proved by shooting argument.