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Propagation and interaction of shock waves of quasilinear equation. (English) Zbl 1008.35041
This paper deals with the weak asymptotic method to study the dynamics of propagation and interaction of shock waves for quasilinear equations in the one-dimensional case. Asymptotic solutions are given and the dynamics of the shock wave merging process is described. It is remarked that the method is also applicable for solving a similar problem in the case of systems of first-order quasilinear equations in one dimension. The paper may be of interest to someone interested in the problem of nonlinear wave interactions for quasilinear equations and systems.
MSC:
35L67Shocks and singularities