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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 PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume112Issue:1Pages:1-32
AbstractFor 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 AreaMathematics
WOS SubjectMathematics
WOS IDWOS:A1994PC23500001
PublisherACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS
Citation statistics
Cited Times:156[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/27842
Collection中国科学院数学与系统科学研究院
Affiliation1.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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