Volume 20, Issue 2, May 2013, Pages 229 - 244
Formation of Delta Standing Wave for a Scalar Conservation Law with a Linear Flux Function Involving Discontinuous Coefficients
Authors
Meina Sun
School of Mathematics and Statistics Science, Ludong University Yantai, Shandong Province, 264025, P. R. China,smnwhy0350@163.com
Received 5 February 2013, Accepted 29 April 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.805573How to use a DOI?
- Keywords
- Delta standing wave; method of characteristics; discontinuous coefficient; nonstrictly hyperbolicity; scalar conservation law
- Abstract
The aim of this paper is to study the formation of delta standing wave for a scalar conservation law with a linear flux function involving discontinuous coefficients. In order to deal with it, we approximate the discontinuous coefficients by piecewise affine ones and then apply the method of characteristics to construct a global solution to the original equation by approximation. Finally, it is proved rigorously that the delta standing wave can be obtained in the limit of the approximate solution as the perturbation parameter tends to zero. In contrast to the classical method of vanishing viscosity, it can be seen clearly here how the delta standing wave forms naturally along the characteristics.
- Copyright
- © 2013 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/).
Cite this article
TY - JOUR AU - Meina Sun PY - 2021 DA - 2021/01/06 TI - Formation of Delta Standing Wave for a Scalar Conservation Law with a Linear Flux Function Involving Discontinuous Coefficients JO - Journal of Nonlinear Mathematical Physics SP - 229 EP - 244 VL - 20 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.805573 DO - 10.1080/14029251.2013.805573 ID - Sun2021 ER -