Global solutions for a simplified shallow elastic fluids model
type: Item
instance of: scholarly article
title: Global solutions for a simplified shallow elastic fluids model
zbMATH Open document ID: 1475.35116
DOI: 10.1155/2014/920248
author: C. Klingenberg
author: Yun-Guang Lu
author: Leonardo Rendón
author: Deyin Zheng
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The Cauchy problem for a simplified shallow elastic fluids model, one \(3 \times 3\) system of Temple's type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Riemann invariant is singular near the zero layer depth \(\left(\rho = 0\right)\). This work extends in some sense the previous works of \textit{D. Serre} [J. Differ. Equations 68, 137--168 (1987; Zbl 0627.35062)] and \textit{R. J. LeVeque} and \textit{B. Temple} [Trans. Am. Math. Soc. 288, 115--123 (1985; Zbl 0561.65067)], which provided the global existence of weak solutions for \(2 \times 2\) strictly hyperbolic system and (Heibig, 1994) for \(n \times n\) strictly hyperbolic system with smooth Riemann invariants.
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 7023309
Wikidata QID: Q59042836
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/920248
OpenAlex ID: W2023018412
cites work: Systems of Conservation Laws with Invariant Submanifolds
cites work: Solutions à variations bornées pour certains systèmes hyperboliques de lois de conservation. (Solutions of bounded variations for certain hyperbolic systems of conservation laws)
cites work: Stability of Godunov's Method for a Class of 2 × 2 Systems of Conservation Laws
cites work: Existence and uniqueness of solutions for some hyperbolic systems of conservation laws
cites work: Q4183803
description: scientific article; zbMATH DE number 7023309