The Structure Of Weak Entropy Solution And L～1-convergence Rate Of Viscosity Methods To The Initial-boundary Value Problem For Scalar Conservation Laws

This thesis is concerned with an initial-boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of weak entropy solution of corresponding initial value problem and the boundary entropy condition which was developed by Bardos-Leroux-Nedelec, we give a construction method to the weak entropy solution of the initial-boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial-boundary value problem includes the following new interaction type: a central rarefaction wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L1-error estimate for viscosity methods to this initial-boundary value problem by using the matching traveling wave solutions method. If the inviscid solution includes the interaction that a central rarefaction wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution isbounded by O in L1-norm; otherwise, as in the initial value problem, the error bound is O.