The Multiplication of Distributions in the Study of a Riemann Problem in Fluid Dynamics

DOI

10.1080/14029251.2017.1341696How to use a DOI?

Keywords

Products of distributions; Isentropic fluid dynamics system; Pressureless gas dynamics system; Shock waves; Delta waves; Delta shock waves

Abstract

The present paper concerns the study of a Riemann problem for the system ut+(12u2+φ(v))x=0,vt+(uv)x=0 , with a one dimensional space variable. We consider φ an entire function that takes real values on the real axis. Under certain conditions, this system provides solutions to the pressureless gas dynamics and the isentropic fluid dynamics systems. We get all solutions of this problem within a convenient space of distributions that contains discontinuous functions and Dirac measures. For this purpose, we use a solution concept defined in the setting of a distributional product. This concept consistently extends the classical solution concept and can also be considered as an extension of the weak solution concept for nonlinear evolution equations. Our product, not defined by approximation processes, can be applied to several physical models.

Copyright

© 2017 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - C.O.R. Sarrico
AU  - A. Paiva
PY  - 2021
DA  - 2021/01/06
TI  - The Multiplication of Distributions in the Study of a Riemann Problem in Fluid Dynamics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 328
EP  - 345
VL  - 24
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1341696
DO  - 10.1080/14029251.2017.1341696
ID  - Sarrico2021
ER  -