The Perturbed Riemann Problem For The Special Keyfitz-Kranzer System With Three Piecewise Constant Initial States

In this thesis,the Riemann problem for some hyperbolic systems of conservation laws is considered.More precisely,we are mainly concerned with the Keyfitz-Kranzer System.We first solve the solutions to the Riemann problem and then constructed the solutions to the perturbed Riemann problem when the initial data are chosen as three piecewise constant states under suitable assumptions.The global solutions to the perturbed Riemann problem are constructed explicitly by studying all occurring wave interactions in details.Furthermore,the stabilities of solutions are obtained under the specific small perturbations of Riemann initial data.The reasech of this thesis has not only extensively physical background,but also has important meanings in theory and extensive prospect in practical application.The structure of this thesis is as follows:The first chapter mainly introduces the related physical background for the Keyfitz-Kranzer system.Then some detailed methods used in this thesis are also delivered,including the basic concepts for hyperbolic systems of conservation laws and the solving method for the Riemann problems,as well as the wave interaction by using the method of characteristics.The second chapter enumerates some basic knowledge,related theorems and definitions,which are used in this thesis.The third chapter is mainly concerned with the construction and stability alalysis of global solutions for the symmetrical Keyfitz-Kranzer system under the appropriate assumptions.The solutions to the Riemann problem for the system are solved and then the solutions to the perturbed Riemann problem are also constructed by study the detailed wave interactions in the phase plane by using the method of characteristics.Finally,the stability of Riemann solution is obtained.In the fourth chapter,we further study the stability of solutions to the perturbed Riemann problem for the special Keyfitz-Kranzer system under the small perturbation of Riemann initial data.The adopted method is also to use three pieces of constant states and then the stability of Riemann solution can be analyzed by letting the perturbed region in the middle tend to zero.The fifth chapter mainly summarizes the conclusions of this thesis and delivers the possible research in the future.