Global Solutions for a Simplified Shallow Elastic Fluids Model
Please always quote using this URN: urn:nbn:de:bvb:20-opus-117978
- The Cauchy problem for a simplified shallow elastic fluids model, one 3 x 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 x 2 strictly hyperbolicThe Cauchy problem for a simplified shallow elastic fluids model, one 3 x 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 x 2 strictly hyperbolic system and (Heibig, 1994) for n x n strictly hyperbolic system with smooth Riemann invariants.…
Author: | Yun-guang Lu, Christian Klingenberg, Leonardo Rendon, De-Yin Zheng |
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URN: | urn:nbn:de:bvb:20-opus-117978 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Abstract and Applied Analytics |
ISSN: | 1687-0409 |
Year of Completion: | 2014 |
Issue: | 920248 |
Source: | Abstract and Applied Analysis Volume 2014, Article ID 920248, 5 pages. doi:10.1155/2014/920248 |
DOI: | https://doi.org/10.1155/2014/920248 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | conservation laws; hyperbolic systems |
Release Date: | 2015/08/29 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung |