Phase Transition Problem For A One-Dimensional System Of Compressible Fluid

In this PaPer,We investigate the Cauchy Problem of nolllinearhyPerbolie-elliPtie system in the Eulerian coordinateswhereu(x,t) is the velocity. v(x,t)>0 is the volume, p = p(v) is the pressure, μ>0 is the viscosity constant, v₀ and u₀ is the initial volume and velocity satisfying Iim(v₀,u₀) = (v,0) and inf(v₀(x))>0, wherev is a positive constant.The equation of state of the fluids p(-) is a C²(0,+∞) function satisfyingfor some positiveconstants k,a^-,v₁,a⁰,v₂ and a⁺,with a^-102+.