Abstract
The problem posed by Gelfand on the asymptotic behavior (in time) of solutions to the Cauchy problem for a first-order quasilinear equation with Riemann-type initial conditions is considered. By applying the vanishing viscosity method with uniform estimates, exact asymptotic expansions in the Cauchy–Gelfand problem are obtained without a priori assuming the monotonicity of the initial data, and the initial-data parameters responsible for the localization of shock waves are described.
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Original Russian Text © G.M. Henkin, A.A. Shananin, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 4, pp. 415–418.
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Henkin, G.M., Shananin, A.A. On the Cauchy–Gelfand problem. Dokl. Math. 92, 731–734 (2015). https://doi.org/10.1134/S106456241506023X
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DOI: https://doi.org/10.1134/S106456241506023X