The delta-shock wave for the two variables of a class of Temple system

The delta-shock wave for the two variables of a class of Temple system

Abstract We investigate the Riemann problem for one-dimensional Temple class, obtain the Riemann solutions containing delta-shock wave, and discover that each variable of this system contains the Dirac delta function in different region. By the interaction of the delta-shock wave with the elementary...

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Main Authors: Guodong Wang, Jia-Bao Liu, Lin Zhao, Mingjun Hu
Format: Article
Language:English
Published: SpringerOpen 2018-07-01
Series:Advances in Difference Equations
Subjects:
Temple class
Riemann problem
Delta-shock wave
Generalized Riemann problem
Online Access:http://link.springer.com/article/10.1186/s13662-018-1708-6
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spelling doaj-3f63f1373af348f58643f908f54721132020-11-25T01:51:05ZengSpringerOpenAdvances in Difference Equations1687-18472018-07-012018111510.1186/s13662-018-1708-6The delta-shock wave for the two variables of a class of Temple systemGuodong Wang0Jia-Bao Liu1Lin Zhao2Mingjun Hu3School of Mathematics and Physics, Anhui Jianzhu UniversitySchool of Mathematics and Physics, Anhui Jianzhu UniversitySchool of Mathematics and Physics, Anhui Jianzhu UniversitySchool of Mathematics and Physics, Anhui Jianzhu UniversityAbstract We investigate the Riemann problem for one-dimensional Temple class, obtain the Riemann solutions containing delta-shock wave, and discover that each variable of this system contains the Dirac delta function in different region. By the interaction of the delta-shock wave with the elementary waves we present the generalized Riemann problem for this system and construct the global solutions. By studying the limits of the solutions as perturbed parameter ε approaches zero we observe that the Riemann solutions are stable for such perturbations of the initial data.http://link.springer.com/article/10.1186/s13662-018-1708-6Temple classRiemann problemDelta-shock waveGeneralized Riemann problem
collection DOAJ
language English
format Article
sources DOAJ
author Guodong Wang
Jia-Bao Liu
Lin Zhao
Mingjun Hu
spellingShingle Guodong Wang
Jia-Bao Liu
Lin Zhao
Mingjun Hu
The delta-shock wave for the two variables of a class of Temple system
Advances in Difference Equations
Temple class
Riemann problem
Delta-shock wave
Generalized Riemann problem
author_facet Guodong Wang
Jia-Bao Liu
Lin Zhao
Mingjun Hu
author_sort Guodong Wang
title The delta-shock wave for the two variables of a class of Temple system
title_short The delta-shock wave for the two variables of a class of Temple system
title_full The delta-shock wave for the two variables of a class of Temple system
title_fullStr The delta-shock wave for the two variables of a class of Temple system
title_full_unstemmed The delta-shock wave for the two variables of a class of Temple system
title_sort delta-shock wave for the two variables of a class of temple system
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2018-07-01
description Abstract We investigate the Riemann problem for one-dimensional Temple class, obtain the Riemann solutions containing delta-shock wave, and discover that each variable of this system contains the Dirac delta function in different region. By the interaction of the delta-shock wave with the elementary waves we present the generalized Riemann problem for this system and construct the global solutions. By studying the limits of the solutions as perturbed parameter ε approaches zero we observe that the Riemann solutions are stable for such perturbations of the initial data.
topic Temple class
Riemann problem
Delta-shock wave
Generalized Riemann problem
url http://link.springer.com/article/10.1186/s13662-018-1708-6
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