## Abstract and Applied Analysis

### Global Solutions for a Simplified Shallow Elastic Fluids Model

#### Abstract

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 $(\rho =0)$. This work extends in some sense the previous works, (Serre, 1987) and (Leveque and Temple, 1985), 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 920248, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412279790

Digital Object Identifier
doi:10.1155/2014/920248

Mathematical Reviews number (MathSciNet)
MR3186987

Zentralblatt MATH identifier
07023309

#### Citation

Lu, Yun-guang; Klingenberg, Christian; Rendon, Leonardo; Zheng, De-Yin. Global Solutions for a Simplified Shallow Elastic Fluids Model. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 920248, 5 pages. doi:10.1155/2014/920248. https://projecteuclid.org/euclid.aaa/1412279790

#### References

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