Global BV solutions to a p-system with relaxation

In this paper, we study the global existence of BV solutions to a p-system with a relaxation source term using the Glimm's scheme. The pressure p is given by a γ-law with γ=1. By a suitable choice of the measure for the strength of the shock waves, we show that the total strength of the waves and the total variation of the solutions are uniformly bounded with respect to the relaxation parameter. Furthermore, when the relaxation parameter tends to zero, we show that the sequence of BV solutions eventually converges to a weak solution to the equilibrium equation. © 2000 Academic Press.