Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws

We consider the Cauchy problem for n x n strictly hyperbolic systems of nonresonant balance laws ut + f(u)(x) = g(x,u), x is an element of R, t>0, u(0,.) = u(0) is an element of L-1 boolean AND BV (R;R-n), \lambda(i)(u)\ greater than or equal to c>0 for all i is an element of {1,..., n}, \g(.,u)\ + parallel todel(u)g(.,u)parallel to less than or equal to omega is an element of L-1 boolean AND L-infinity (R), each characteristic field being genuinely nonlinear or linearly degenerate. Assuming that parallel toomegaparallel to(L 1(R)) and parallel tou(0)parallel to(BV(R)) are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of special wave-front tracking approximations for which the source term is localized by means of Dirac masses. Moreover, we give a characterization of the resulting semigroup trajectories in terms of integral estimates.