Comparision of the definitions of generalized solution of the Cauchy problem for quasi-linear equation
Mathematical Physics
2017-01-04 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1701.00719,
title = {Comparision of the definitions of generalized solution of the Cauchy problem for quasi-linear equation},
author = {Alexander Gasnikov},
journal= {arXiv preprint arXiv:1701.00719},
year = {2017}
}
Comments
Preprint CCAS RAS, 2006 (3-d edition, 2016); 75 pages, in Russian