Baiti, P.; Bressan, A. The semigroup generated by a Temple class system with large data. (English) Zbl 0890.35083 Differ. Integral Equ. 10, No. 3, 401-418 (1997). Summary: We consider the Cauchy problem \[ u_t + [F(u)]_x =0, \quad u(0,x) = \bar u(x) \] for a nonlinear \(n\times n\) system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinate system made of Riemann invariants, we prove the existence of a weak solution that depends in a Lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation. Cited in 25 Documents MSC: 35L65 Hyperbolic conservation laws 35D05 Existence of generalized solutions of PDE (MSC2000) 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:conservation laws; weak solutions; coinciding shock and rarefaction curves; Riemann invariants PDFBibTeX XMLCite \textit{P. Baiti} and \textit{A. Bressan}, Differ. Integral Equ. 10, No. 3, 401--418 (1997; Zbl 0890.35083)