| This article is devoted to research the convergence behavior of Riemann solutions to the Extended Chaplygin gas nonsymmetric Keyfitz-Kranzer system in the pressure disappearance limit process.By using the phase plane and the characteristic analysis method,the Riemann solutions of the associated equations is constructed,further prove the limit of solution respectively when A,B?0 and A?0.Firstly,we consider the limiting of the solutions to the Extended Chaplygin gas Keyfitz-Kranzer system as A,B?0.When u-<u+,the solutions consisting of rarefaction wave and contact discontinuity converges to two contact discontinuity,the intermediate state tends to vacuum state.Moreover,when u->u+,the solutions containing the shock wave and contact discontinuity converges to a special ?shock wave,whose wave speed and weight are different from that of the pressureless flow,and the middle density tends to the singular measure.Subsequently,the perturbed Keyfitz-Kranzer system are introduced to construct the Riemann solution,and it is proved that the perturbed system converges to the zero pressure flow as A,B?0.Secondly,we discuss the limit of the solutions to the Extended Chaplygin gas Keyfitz-Kranzer system with source term as A?0.For u-<u++B/?+,the solutions consists of rarefaction wave and contact discontinuity converges to two contact discontinuity,the intermediate state does not tend to vacuum state.However,for u->u++B/?+,the solutions contains the shock wave and contact discontinuity converges to a peculiar ? shock wave,whose wave velocity and weight are different from that of the Chaplygin gas system,and the middle density tends to the singular measure.Then we introduce into the perturbed Keyfitz-Kranzer system with source term and structure the Riemann solution,and it is proved that the perturbed system with source term tends to the Chaplygin gas system as A?0.Thirdly,the theoretical results are verified by numerical simulation. |
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