In this work, we consider the convergence of the zero viscosity method to some 2x2systems in conservation laws, namely , the so-called p-system and the Keyfitz -Kranzersystem. We give the improved convergence results when the underlying inviscid solutionhas finitely many noninteracting shocks and rarefactions with no small restrictionon theinitial BV data, and we also prove that for a special 2x2 system, the stability of theshock profile can be attained in the L1 space and without small restriction on the shockstrength and the initial perturbation. The main method we use is the energy estimatecombined with different techniques in different subjects. Moreover, we consider the boundary regularity of the Tricomi equation as a beginningof the study on the mixed type partial differential equations and the transonic waves,and we obtained the continuity of the first order normal derivative on the boundary and at the corners when the boundary value is merely continuous. The method we use is thefundamental solution method.