Global existence and strong trace property of entropy solutions by the source-concentration Glimm scheme for nonlinear hyperbolic balance laws

Abstract

In this paper, we investigate the initial-boundary value problem for a nonlinear hyperbolic system of balance laws with source terms axg and ath. We assume that the boundary data satisfy a linear or smooth nonlinear relation. The generalized Riemann and boundary Riemann solutions are provided with the variation of a concentrated on a thin T -shaped region in each grid. We generalize Goodman's boundary interaction estimates [7], introduce a new version of Glimm scheme to construct the approximation solutions, and provide their stability by considering two types of functions of a(x, t). The global existence of entropy solutions is established. Under some sampling condition, we find the entropy solutions converge to their boundary values in L 1 loc as x approaches the boundary. In addition, such boundary values match the boundary condition almost everywhere in t.