Analysis Of The Stability Of Solution Of The Two Types Of Conservation Law Equations

This dissertation is devoted to the comparison between the entropy solution of the problem that two-dimensional steady isentropic flow past a duct and the solution of the quasi-one-dimensional problem. At first, we prove by a modified Glimm-scheme that the local entropy solution in the supersonic region of the first problem exists, when the boundaries of the duct are small perturbations of lines. Then based on it, we give an estimation on the difference between this local entropy solution and the solution of the quasi-one-dimensional problem in L2 norm. In the last part of this dissertation, using Lax - Friedrichs difference scheme, we discuss the stability problem on flow function and relaxation function of a class of conservation law systems with a source term and a relaxation term.