Vanishing Pressure And Flux-perturbation Limits Of Solutions To The Nonsymmetric KK System

This thesis studies the limits of Riemann solutions to the nonsymmetric Keyfitz-Kranzer system as the pressure and flux perturbation vanish. Using the characteristic and phase plane analysis methods, the Riemann problems of the corresponding systems are constructively solved. Furthermore, we discuss the limiting behaviors of Riemann solutions as the pressure and flux perturbation vanish, respectively.Chapter 1 presents research status of the nonsymmetric Keyfitz-Kranzer system and the work of the thesis.Chapter 2 reviews the delta-shock and vacuum solutions of the zero-pressure flow.Chapter 3 studies the vanishing pressure limits of Riemann solutions of the Keyfitz-Kranzer system. We firstly prove that, as the pressure vanishes, any Riemann solution containing a shock wave and a contact discontinuity tends to a delta shock wave, whose propagation speed and strength are different from those of the zero-pressure flow; any Riemann solution containing a rarefaction wave and a contact discontinuity with a non-vacuum intermediate state tends to a vacuum state of the zero-pressure flow. Secondly, we solve the Riemann problem of the perturbed Keyfitz-Kranzer system and four differ-ent configurations of Riemann solutions are constructed. Then, it is proved that, as the pressure vanishes, any Riemann solution of this perturbed system containing two shock waves tends to the delta-shock solution to the zero-pressure flow; any Riemann solution containing two rarefaction waves tends to the vacuum state to the zero-pressure flow.Chapter 4 discusses the vanishing flux-perturbation limits of Keyfitz-Kranzer system. The Riemann problem of the flux-perturbation system is firstly solved and four different configurations of Riemann solutions are obtained. Then we prove that, as flux perturbation vanishes, any Riemann solution containing two shock waves tends to a delta-shock solution, whose propagation speed and strength, however, are different from those of the zero-pressure flow; any Riemann solution involving two rarefaction waves tends to a vacuum state of the zero-pressure flow. Finally, we study the vanishing flux-perturbation limits of the perturbed Keyfitz-Kranzer system. Based on solving the Riemann problem of this perturbed system, we prove that, as flux perturbation vanishes, any Riemann solution of this perturbed system involving two shock waves tends to a delta-shock solution; any Riemann solution containing two rarefaction waves tends to a vacuum state solution.