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arXiv · 1701.00719

Comparision of the definitions of generalized solution of the Cauchy problem for quasi-linear equation

Alexander Gasnikov
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Abstract

In preprint we consider and compare different definitions of generalized solution of the Cauchy problem for 1d-scalar quasilinear equation (conservation law). We start from the classical approaches goes back to I.M. Gelfand, O.A. Oleinik, S.N. Kruzhkov and move to the modern finite-difference approximations approaches belongs to A.A. Shananin and G.M. Henkin. We discuss the conditions that provide definitions to be equivalent.

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Alexander Gasnikov. 2017-01-02. Comparision of the definitions of generalized solution of the Cauchy problem for quasi-linear equation. https://arxiv.org/abs/1701.00719

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