The semigroup generated by a Temple class system with large data. (English) Zbl 0890.35083

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.


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