The Continuous Weak Entropy Solution And The L～1 Convergence Rate Of Its Viscosity Approximations For The Initial-boundary Problem Of Scalar Conservation Laws

This thesis is concerned with the global continuous weak entropy solution and the L~1 convergence rate of its viscosity approximations for the initial-boundary problem of scalar conservation laws. We give a sufficient condition that its global continuous weak entropy solution exists and is unique for the initial-boundary problem of scalar convex conservation laws, and construct this continuous weak entropy solution by the truncation method, and obtain its boundary behaviors. According to the structure of the weak entropy solution, we derive a convergence rate for its viscosity approximations to the inviscid solution in L~1 norm by using the L~1 -stability lemma for nonhomogeneous viscous equations with initial-boundary conditions.