Initial-Boundary Value Problems for Conservation Laws

We establish some general concepts concerning boundary conditions for systems of conservation laws defined on one-dimensional space intervals, and prove some general results. Among these is an extension of Glimmʹs existence theorem to initial-boundary value problems. We also prove the convergence of the time averages of the solutions to certain initial-boundary value problems for systems arising in fluid flows in porous media, isentropic gas dynamics, and elasticity theory.