Riemann Problems and Exact Solutions for the p-System

Natale Manganaro and Alessandra Rizzo
Additional contact information
Natale Manganaro: Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy
Alessandra Rizzo: Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy

Mathematics, 2022, vol. 10, issue 6, 1-15

Abstract: In this paper, within the framework of the Method of Differential Constraints, the celebrated p-system is studied. All the possible constraints compatible with the original governing system are classified. In solving the compatibility conditions between the original governing system and the appended differential constraint, several model laws for the pressure p ( v ) are characterised. Therefore, the analysis developed in the paper has been carried out in the case of physical interest where p = p 0 v − γ , and an exact solution that generalises simple waves is determined. This allows us to study and to solve a class of generalised Riemann problems (GRP). In particular, we proved that the solution of the GRP can be discussed in the ( p , v ) plane through rarefaction-like curves and shock curves. Finally, we studied a Riemann problem with structure and we proved the existence of a critical time after which a GRP is solved in terms of non-constant states separated by a shock wave and a rarefaction-like wave.

Keywords: Riemann problems; p-system; exact solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/6/935/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/6/935/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:6:p:935-:d:771330

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().