Large time behavior of periodic solutions of hyperbolic systems of conservation laws (Q1898798)

The initial problem for a system of \(m\) conservation laws is considered, the system being strictly hyperbolic and genuinely nonlinear in the sense of \textit{P. D. Lax} [Commun. Pure Appl. Math. 10, 537--566 (1957; Zbl 0081.08803)]. The theory of generalized characteristics by the author [Arch. Ration. Mech. Anal. 107, No. 2, 127--155 (1989; Zbl 0714.35046)] is utilized. The large time behavior of solutions under periodic initial data with mean zero is investigated.