L~1-Convergence Rates For Relaxation Approximations To Conservation Laws With Boundary

This thesis is concerned with L~1-convergence rate for solutions of the stiff relaxation system with the initial-boundary value condition to its equilibrium solutions.Under the condition that the boundary data is a nontransonic state and the initial data is small perturbations of this nontransonic state,by using matching method and the traveling wave solutions,we derive an error between the relaxation approximations and its equilibrium solutions is bounded by O(ε|Inε|+ε) in L~1 -norm if the equilibrium solutions are piecewise smooth with finitely many discontinuities for the initial-boundary value problem of the stiff relaxation system.