An extension of Bakhvalov’s theorem for systems of conservation laws with damping

Abstract

For [Formula: see text] systems of conservation laws satisfying Bakhvalov conditions, we present a class of damping terms that still yield the existence of global solutions with periodic initial data of possibly large bounded total variation per period. We also address the question of the decay of the periodic solution. As applications, we consider the systems of isentropic gas dynamics, with pressure obeying a [Formula: see text]-law, for the physical range [Formula: see text], and also for the “non-physical” range [Formula: see text], both in the classical Lagrangian and Eulerian formulation, and in the relativistic setting. We give complete details for the case [Formula: see text], and also analyze the general case when [Formula: see text] is small. Further, our main result also establishes the decay of the periodic solution.