Conditions of Osgood type in uniqueness problem for generalized entropy solution to Cauchy problem for quasilinear first order equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 0966.35077
publication date: 2001-06-25T00:00:00Z
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1609704
zbMATH Keywords: main uniqueness condition
author: S. N. Kruzhkov
author: Evgeniy Panov
MaRDI profile type: Publication
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title: Conditions of Osgood type in uniqueness problem for generalized entropy solution to Cauchy problem for quasilinear first order equations
published in: Vestnik Rossiĭskogo Universiteta Druzhby Narodov. Seriya Matematika
review text: The paper deals with the problem of uniqueness of generalized entropy solutions to the Cauchy problem in nonlocal statements for the conservation law of the form NEWLINE\[NEWLINE \begin{gathered} u_t+\text{div}_x\phi(u) = 0,\quad x=(x_1,\dots,x_n)\in \mathbb{R}^n,\quad t\in \mathbb{R}^1,\\ u\equiv u(t,x),\quad \phi(u)\equiv(\phi_1(u),\dots,\phi_n(u))\in \mathbb{R}^n,\quad \phi_i(u)\in C(\mathbb{R}^1) \end{gathered} NEWLINE\]NEWLINE in the layer \((0,T]\times \mathbb{R}^n \) with the initial condition \(u(0,x) = u_0(x)\in L_\infty(\mathbb{R}^n)\). It is assumed that the main uniqueness condition characterizing ``total smoothness'' of flow functions has the form of the integral condition of Osgood type known in the theory of ODE.
reviewed by: A. A. Martynyuk
description: scientific article; zbMATH DE number 1609704