Interaction Between Delta-shock And Classical Waves For Isentropic Euler Equations With General Pressure

In this thesis,we consider the isentropic Euler equations with general pressure including Chaplygin gas as important examples,and study the limit behavior of Riemann solutions when the pressure vanishes.Furthermore,with the characteristic and phase plane analysis methods,a series of Riemann solutions with different geometric structures are obtained by studying the interaction between delta-shock and classical waves.First of all,we review the Riemann problem of zero pressure flow with two constant states.The Riemann solutions include delta shock wave and vacuum.Secondly,based on the five types of Riemann solutions to the isentropic Euler equations with general pressure,it is proved that,when the pressure vanishes,the delta shock solution,or the Riemann solution containing two shock waves of the equations converges to the delta shock solution to the zero pressure flow;the Riemann solution containing two rarefaction waves of the equations converges to the vacuum solution to the zero pressure flow.Finally,the initial value problem of the isentropic Euler equations with general pressure in three constant states is considered.With the help of the generalized Rankine-Hugoniot condition and entropy condition,17 different Riemann solution structures are obtained by studying the interaction between delta-shock and classical waves.