Substantiation of the method of internal averaging along the characteristics of weakly linear systems. II
type: Item
instance of: scholarly article
title: Substantiation of the method of internal averaging along the characteristics of weakly linear systems. II
zbMATH Open document ID: 0729.65070
DOI: 10.1007/BF00966457
author: A. V. Krylov
published in: Lithuanian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: [For part I see ibid. 29, No.4, 721-732 (1989; Zbl 0711.65081).] The method of internal averaging is generalized to systems having non- uniform integral average. Firstly, the averaging in the class of functions with non-uniform integral average is studied. Then the existence and uniqueness of the solutions of averaged problems are proved. In the last part of the work averaged equations with different classes of initial conditions are investigated. The method described is applicable to a larger class of problems than semi-linear systems of first-order partial differential equations.
Mathematics Subject Classification ID: 65M25
Mathematics Subject Classification ID: 35F25
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 4205912
zbMATH Keywords: weakly linear systems
zbMATH Keywords: first-order hyperbolic systems
zbMATH Keywords: method of characteristics
zbMATH Keywords: method of internal averaging
zbMATH Keywords: non-uniform integral average
zbMATH Keywords: semi-linear systems
reviewed by: Yuri I. Shokin
MaRDI profile type: Publication
cites work: Q3495579
cites work: Q3681250
cites work: Q3092574
cites work: Q3027479
description: scientific article; zbMATH DE number 4205912