The Vanishing Pressure Limit Of Riemann Solutions And Shadow Wave Solution For One-dimensional Euler Equations

In this thesis,the limit behavior of Riemann solutions to the non-isentropic gen-eralized Chaplygin gas equations is firstly studied.In the next place,the shadow wave solution of isentropic Chaplygin gas equations with a body force is considered.The first chapter presents research status of Euler equations for non-isentropic fluids and shadow wave,and introduces the main work of this thesis.The second chapter briefly reviews the Riemann solutions of transport equations.The third chapter studies the vanishing pressure limit of Riemann solutions to the non-isentropic generalized Chaplygin gas equations,there are the phenomena of concen--tration and cavitation.The Riemann solutions are composed of backward（forward）cen-tered rarefaction waves（?）。contact discontinuity Jε,backward（forward）shock waves（?）and delta shock wave.In the case of u₊<u_-,we rigorously prove that Riemann solution including（?）and Jε for the non-isentropic generalized Chaplygin gas equations converges to delta shock wave solution of pressureless Euler equations,both the density and the internal energy simultaneously present a Dirac delta singularity,and obtain the entropy consistency.Moreover,in the case of u₊>u_-,the Riemann solution involving（?）and Jε converges to the solution involving two contact discontinuities of pressure-less Euler equations,the non-vacuum state between（?）and（?）tends to vacuum state.Finally,the theoretical analysis in the second and third sections is verified by numerical simulations.The fourth chapter mainly discusses the shadow wave solution of isentropic Chap-lygin gas dynamics system with a body force.In the first place,we perturb the prop-agation speed of a wave from both sides by a small enough parameter ε,so that left state and right state of the anticipated solution are connected by two shock waves,some variables in the intermediate state are of the same order as ε^-1,so we construct shadow wave solution.On this basis,in order to ensure the weak uniqueness of the shadow wave solution,we use the over-compressive entropy condition as an admissibility criteria.It is found that the over-compressive shadow wave solution of isentropic Euler equations with a body force converges to the delta shock wave solution of corresponding Riemann problem.