Concentration of source terms in generalized Glimm scheme for global entropy solutions of nonlinear hyperbolic balance laws

In this paper, we investigate the Cauchy problem for a nonlinear hyperbolic system of balance laws with sources axg and ath. To get the approximate solutions of our problem, we consider a version of generalized Riemann problem that concentrates the variation of a on a thin T-shaped region of each grid. A new version of Glimm scheme is introduced to construct the approximate solutions and its stability is proved by considering two types of conditions on a. Finally, we verify the consistency of the scheme and the entropy inequality to establish the global existence of entropy solutions.