Global BV Entropy Solutions and Uniqueness for Hyperbolic Systems of Balance Laws

Abstract

We consider the Cauchy problem for n×n strictly hyperbolic systems of nonresonant balance laws

each characteristic field being genuinely nonlinear or linearly degenerate. Assuming that and 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.