This research explores the initial-boundary value problem for the 2 × 2 hyperbolic systems of balance laws whose sources are the time-dependent and contain the integral of unknowns. Perturbed Riemann and boundary Riemann problems are provided to account for the time-dependence of sources. Their approximation solutions are constructed by modified Lax's method. In addition, we introduce a new version of Glimm scheme (GGS) and study its stability which is proved by the wave interaction estimates in a dissipativity assumption. With the consistency of GGS, the existence of a global weak solution satisfying the entropy inequality is then achieved. Finally the Lipschitz continuous solution to the problem is established by the weak convergence of the residual.
|頁（從 - 到）
|Nonlinear Analysis, Theory, Methods and Applications
|已出版 - 10月 2012