KMS Of Academy of mathematics and systems sciences, CAS
DELTA-SHOCK WAVES AS LIMITS OF VANISHING VISCOSITY FOR HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS | |
TAN, DC; ZHANG, T; CHANG, T; ZHENG, YX | |
1994-08-01 | |
Source Publication | JOURNAL OF DIFFERENTIAL EQUATIONS |
ISSN | 0022-0396 |
Volume | 112Issue:1Pages:1-32 |
Abstract | For simple models of hyperbolic systems of conservation laws, we study a new type of nonlinear hyperbolic wave, a delta-shock wave, which is a Dirac delta function supported on a shock. We prove that delta-shock waves are w*-limits in L1 of solutions to some reasonable viscous perturbations as the viscosity vanishes. Further, we solve the multiplication problem of a delta function with a discontinuous function to show that delta-shock waves satisfy the equations in the sense of distributions. Under suitable generalized Rankine-Hugoniot and entropy conditions, we establish the existence and uniqueness of solutions involving delta-shock waves for the Riemann problems. The existence of solutions to the Cauchy problem is also investigated. (C) 1994 Academic Press, Inc. |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:A1994PC23500001 |
Publisher | ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/27842 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 1.CHINESE ACAD SCI,INST MATH,BEIJING,PEOPLES R CHINA 2.INDIANA UNIV,INST MATH,BLOOMINGTON,IN 47405 |
Recommended Citation GB/T 7714 | TAN, DC,ZHANG, T,CHANG, T,et al. DELTA-SHOCK WAVES AS LIMITS OF VANISHING VISCOSITY FOR HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,1994,112(1):1-32. |
APA | TAN, DC,ZHANG, T,CHANG, T,&ZHENG, YX.(1994).DELTA-SHOCK WAVES AS LIMITS OF VANISHING VISCOSITY FOR HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS.JOURNAL OF DIFFERENTIAL EQUATIONS,112(1),1-32. |
MLA | TAN, DC,et al."DELTA-SHOCK WAVES AS LIMITS OF VANISHING VISCOSITY FOR HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS".JOURNAL OF DIFFERENTIAL EQUATIONS 112.1(1994):1-32. |
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