The Limiting Behavior Of The Riemann Solution To The Euler System With The Logarithmic Equation

In this dissertation,Riemann problems of homogeneous and nonhomogeneous Euler systems with the logarithmic equation are studied completely.With the analysis method on the phase plane and characteristic analysis approach,all Riemann solutions are obtained constructively.We analyze the formation mechanism of deltashock and vacuum state in the process of the vanishing pressure limit.Significantly,all systems that they converge are 3 × 3.The first chapter presents a more detailed review on delta shock waves and the work of this thesis.The second chapter recalls the Riemann problem for homogeneous 3 × 3 zeropressure dynamical system,and studies the Riemann problem for non-homogeneous zero-pressure dynamical systems.The third chapter solves the Riemann problem of homogeneous Euler system with the logarithmic equation of state.Four kinds of solutions are obtained.With the method of vanishing pressure limit,we prove that,as the pressure disappears,any two-shock and one contact Riemann solution tends to a delta shock wave solution to the zero-pressure flow;any two rarefaction-wave and one contact Riemann solution tends to vacuum state to the zero-pressure flow.The numerical simulations about delta shock waves and vacuum completely are coinciding with theoretical analysis.The last chapter considers the Riemann problem of nonhomogeneous Euler system with the logarithmic equation of state.We prove that,as the pressure vanishes,any two-shock and one contact Riemann solution tends to a delta shock wave solution to the zero-pressure flow with a source term;any two rarefaction-wave and one contact Riemann solution tends to vacuum state to the zero-pressure flow with a source term.