On the piewise smooth solutions to non-homogeneous scalar conservation laws

Yan Xiang Kan; Tao TANG; Zhen Huan Teng

doi:10.1006/jdeq.2000.3962

On the piewise smooth solutions to non-homogeneous scalar conservation laws

Yan Xiang Kan, Tao TANG^*, Zhen Huan Teng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise smooth entropy solution along the generalized characteristics. These estimates play important roles in obtaining the optimal rate of convergence for various approximation methods to conservation laws.

Original language	English
Pages (from-to)	27-50
Number of pages	24
Journal	Journal of Differential Equations
Volume	175
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.2000.3962
Publication status	Published - 1 Sept 2001

Scopus Subject Areas

Analysis
Applied Mathematics

User-Defined Keywords

Generalized characteristics
Non-homogeneous conservation laws
Piecewise smooth solution
Shock

Access to Document

10.1006/jdeq.2000.3962

Cite this

@article{5d8da82857e841d3aa0540abfda21981,

title = "On the piewise smooth solutions to non-homogeneous scalar conservation laws",

abstract = "We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise smooth entropy solution along the generalized characteristics. These estimates play important roles in obtaining the optimal rate of convergence for various approximation methods to conservation laws.",

keywords = "Generalized characteristics, Non-homogeneous conservation laws, Piecewise smooth solution, Shock",

author = "Kan, {Yan Xiang} and Tao TANG and Teng, {Zhen Huan}",

note = "Funding Information: 1The research of this author was supported by the Research Grants Council of Hong Kong and Hong Kong Baptist University. 2The research of the third author was supported by the China State Major Key Project for Basic Research.",

year = "2001",

month = sep,

day = "1",

doi = "10.1006/jdeq.2000.3962",

language = "English",

volume = "175",

pages = "27--50",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - On the piewise smooth solutions to non-homogeneous scalar conservation laws

AU - Kan, Yan Xiang

AU - TANG, Tao

AU - Teng, Zhen Huan

N1 - Funding Information: 1The research of this author was supported by the Research Grants Council of Hong Kong and Hong Kong Baptist University. 2The research of the third author was supported by the China State Major Key Project for Basic Research.

PY - 2001/9/1

Y1 - 2001/9/1

N2 - We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise smooth entropy solution along the generalized characteristics. These estimates play important roles in obtaining the optimal rate of convergence for various approximation methods to conservation laws.

AB - We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise smooth entropy solution along the generalized characteristics. These estimates play important roles in obtaining the optimal rate of convergence for various approximation methods to conservation laws.

KW - Generalized characteristics

KW - Non-homogeneous conservation laws

KW - Piecewise smooth solution

KW - Shock

UR - http://www.scopus.com/inward/record.url?scp=0035454992&partnerID=8YFLogxK

U2 - 10.1006/jdeq.2000.3962

DO - 10.1006/jdeq.2000.3962

M3 - Journal article

AN - SCOPUS:0035454992

SN - 0022-0396

VL - 175

SP - 27

EP - 50

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

On the piewise smooth solutions to non-homogeneous scalar conservation laws

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this