Uniqueness results for diagonal hyperbolic systems with large and monotone data (Q2857732)

The authors study one-dimensional hyperbolic diagonal systems. Initial distribution is non-decreasing and possesses the derivative from the Zygmund space. Global existence of a continuous solution is already proven by the authors [J. Hyperbolic Differ. Equ. 7, No. 1, 139--164 (2010; Zbl 1198.35143)]; in this article the focus is uniqueness. Existence result is also presented. The authors prove uniqueness of continuous vanishing viscosity solutions for strictly hyperbolic system and then existence and uniqueness of Lipschitz solutions for not necessarily strictly hyperbolic system. Applications to one dimensional isentropic gas dynamics is discussed.