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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.

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
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