Interaction Of Delta Shock Waves And Classical Waves For The Generalized Chaplygin Gas Equations

The Chaplygin gas can be used to interpret the relationship between dark matter and dark energy in the universe, and describe the phenomenon of the current accelerated inflation of the universe. In this thesis, we study the interactions of delta shock waves and classical waves for the isentropic generalized Chaplygin gas equations.Firstly, we solve the Riemann problem of the generalized Chaplygin gas equations with initial data of two constant states. Using the phase plane and characteristic analysis methods, five different configurations of Riemann solutions containing delta shock wave; are obtained. Secondly, under the suitable generalized Rankine-Hugoniot relation and en-tropy condition, by investigating the interactions of delta shock waves and classical waves, thirteen kinds of different structures of solutions are constructed, and the corresponding criteria are given. Finally, the numerical simulations obtained by using the second-order nonoscillatory central scheme confirm the theoretical analysis.