On the attainable set for a class of triangular systems of conservation laws. (English) Zbl 1336.35231
The authors describe the attainable set for solutions of special triangular systems of conservation laws consisting of linear continuity equations \((v_i)_t+(g_i(u)v_i)_x=0\), \(i=1,\dots,m\), coupled with a genuinely nonlinear conservation law \(u_t+f(u)_x=0\). After minor modifications such systems includes in particular the classical Keyfitz-Kranzer systems. The authors construct the backward solutions and prove that they are admissible forward solution whenever the target data are attainable. In particular, this implies that the constructed solutions are isentropic. Results of numerical experiments are also presented.
Reviewer: Evgeniy Panov (Novgorod)
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35R30 | Inverse problems for PDEs |
| 47J35 | Nonlinear evolution equations |
Keywords:
backward solutions; isentropic solutions; continuity equation; renormalization property; Keyfitz-Kranzer system; numerical backward resolutionReferences:
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