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Volumn 112, Issue 1, 1994, Pages 1-32

Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws

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EID: 0002178812     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1006/jdeq.1994.1093     Document Type: Article
Times cited : (259)

References (33)
  • 1
    • 0346440753 scopus 로고
    • Un phenomene de concentration evanescente pour des flots non-stationnaires incomprissibles en dimension deux
    • S. Alinhac, Un phenomene de concentration evanescente pour des flots non-stationnaires incomprissibles en dimension deux, Comm. Math. Phys. 127 (1990), 585-596.
    • (1990) Comm. Math. Phys , vol.127 , pp. 585-596
    • Alinhac, S.1
  • 2
  • 3
    • 0003835038 scopus 로고
    • The Riemann problem and interaction of waves in gas dynamics
    • Longman Scientific and Technical, Essex
    • Tung Chang (Tong Zhang) and Ling Hsiao, The Riemann problem and interaction of waves in gas dynamics, Pitman Monographs, No. 41, Longman Scientific and Technical, Essex, 1989.
    • (1989) Pitman Monographs , Issue.41
    • Chang, T.1    Hsiao, L.2
  • 4
    • 0015746230 scopus 로고    scopus 로고
    • Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by viscosity method
    • C. M. Dafermos, Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by viscosity method, Arch. Rational Mech. Anal. 52, 1-9.
    • Arch. Rational Mech. Anal , vol.52 , pp. 1-9
    • Dafermos, C.M.1
  • 5
    • 0040094984 scopus 로고
    • The Riemann problem for certain classes of hyperbolic systems of conservation laws
    • C. M. Dafermos and R. J. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws, J. Differential Equations 20 (1976), 90-114.
    • (1976) J. Differential Equations , vol.20 , pp. 90-114
    • Dafermos, C.M.1    Diperna, R.J.2
  • 6
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • R. DiPerna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511-547.
    • (1989) Invent. Math , vol.98 , pp. 511-547
    • Diperna, R.1    Lions, P.L.2
  • 7
    • 85027600200 scopus 로고    scopus 로고
    • On the Cauchy problem by Balzman equation: Global existence and weak stability
    • to appear
    • R. DiPerna and P. L. Lions, On the Cauchy problem by Balzman equation: Global existence and weak stability, Ann. of Math, to appear
    • Ann. Of Math
    • Diperna, R.1    Lions, P.L.2
  • 8
    • 0010125090 scopus 로고
    • “Seminaire DEP, Ecole Polytechnique 1987-1988, Palaiseau
    • see also C. R. Acad. Sci. Paris 306 (1988), 343-346, and in “Seminaire DEP, Ecole Polytechnique 1987-1988, Palaiseau.
    • (1988) C. R. Acad. Sci. Paris , vol.306 , pp. 343-346
  • 9
    • 84966225077 scopus 로고
    • Reduced Hausdorff dimension and concentration- cancellation for 2-D incompressible flow
    • R. DiPerna and A. Majda, Reduced Hausdorff dimension and concentration- cancellation for 2-D incompressible flow, J. Am. Math. Soc. 1 (1988), 59-95.
    • (1988) J. Am. Math. Soc , vol.1 , pp. 59-95
    • Diperna, R.1    Majda, A.2
  • 11
    • 84990613865 scopus 로고
    • On DiPema-Majda concentration sets for two dimensional incompressible flow
    • C. Greengard and E. Thomann, On DiPema-Majda concentration sets for two dimensional incompressible flow, Comm. Pure Appl. Math. 41 (1988), 295-303.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 295-303
    • Greengard, C.1    Thomann, E.2
  • 12
    • 84980078224 scopus 로고    scopus 로고
    • The partial differential equation u1 + uux = μuxx
    • xx, Comm. Pure Appl. Math. 3, 201-230.
    • Comm. Pure Appl. Math , vol.3 , pp. 201-230
    • Hopf, E.1
  • 13
    • 0038751468 scopus 로고
    • J. Glimm and A. Majda, Eds.), IMA, Volumes in Mathematics and Its Applications, Springer-Verlag, Berlin/New York
    • J. Hunter, in “Multidimensional Hyperbolic Problems and Computations,” (J. Glimm and A. Majda, Eds.), IMA, Volumes in Mathematics and Its Applications, Vol. 29, Springer-Verlag, Berlin/New York, 1991.
    • (1991) Multidimensional Hyperbolic Problems and Computations , vol.29
    • Hunter, J.1
  • 14
    • 0042031547 scopus 로고
    • A viscosity approximation to system of conservation laws with no classical Riemann solution
    • Lecture Notes in Mathematics, Springer-Verlag, Berlin/New York
    • B. L. Keyfitz and H. C. Kranzer, A viscosity approximation to system of conservation laws with no classical Riemann solution in “Nonlinear Hyperbolic Problems,” Lecture Notes in Mathematics, Vol. 1042, Springer-Verlag, Berlin/New York, 1989.
    • (1989) Nonlinear Hyperbolic Problems , vol.1042
    • Keyfitz, B.L.1    Kranzer, H.C.2
  • 17
    • 0000220623 scopus 로고
    • First order quasilinear equations with several space variables
    • S. Kruzkov, First order quasilinear equations with several space variables, Math. Sb. 123 (1970), 228-255
    • (1970) Math. Sb , vol.123 , pp. 228-255
    • Kruzkov, S.1
  • 19
    • 84980077727 scopus 로고
    • Hyperbolic systems of conservation laws, II
    • P. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10 (1957), 537-556.
    • (1957) Comm. Pure Appl. Math , vol.10 , pp. 537-556
    • Lax, P.1
  • 21
    • 85027602042 scopus 로고    scopus 로고
    • Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data
    • A. Majda and Yuxi Zheng, Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data, to appear in Comm. Pure Appl. Math.
    • To Appear in Comm. Pure Appl. Math
    • Majda, A.1    Zheng, Y.2
  • 22
    • 0000695165 scopus 로고
    • Nonlinear superposition and absorption of delta waves in one space dimension
    • J. Rauch and M. C. Reed, Nonlinear superposition and absorption of delta waves in one space dimension, J. Fund. Anal. 73 (1987), 158-178.
    • (1987) J. Fund. Anal , vol.73 , pp. 158-178
    • Rauch, J.1    Reed, M.C.2
  • 23
    • 85027602775 scopus 로고    scopus 로고
    • Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws
    • Dechun Tan and Tong Zhang, Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws, J. Differential Equations, in press.
    • J. Differential Equations
    • Tan, D.1    Zhang, T.2
  • 24
    • 0001168879 scopus 로고
    • The space BV and quasilinear equations
    • A. I. Vol’pert, the space BV and quasilinear equations, Math. USSR-Sb. 2 (1967), 225-267.
    • (1967) Math. Ussr-Sb , vol.2 , pp. 225-267
    • Vol’Pert, A.I.1
  • 26
    • 0001636335 scopus 로고
    • The Riemann problem in two space dimensions for a single conservation law
    • D. Wagner, The Riemann problem in two space dimensions for a single conservation law, SIAM J. Math. Anal. 14 (1983), 534-559.
    • (1983) SIAM J. Math. Anal , vol.14 , pp. 534-559
    • Wagner, D.1
  • 27
    • 0000329914 scopus 로고
    • Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems
    • Tong Zhang and Yuxi Zheng, Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems, SIAM J. Math. Anal. 21 (1990), 593-630.
    • (1990) SIAM J. Math. Anal , vol.21 , pp. 593-630
    • Zhang, T.1    Zheng, Y.2
  • 28
    • 84966244791 scopus 로고
    • Two dimensional Riemann problem for a single conservation law
    • Tong Zhang and Yuxi Zheng, Two dimensional Riemann problem for a single conservation law, Trans. Amer. Math. Soc. 312 (1989), 589-619.
    • (1989) Trans. Amer. Math. Soc , vol.312 , pp. 589-619
    • Zhang, T.1    Zheng, Y.2
  • 29
    • 0039997199 scopus 로고
    • Concentration-cancellation for the velocity in two dimensional incompressible fluid flows
    • Yuxi Zheng, Concentration-cancellation for the velocity in two dimensional incompressible fluid flows, Comm. Math. Phys. 135 (1991), 581-595.
    • (1991) Comm. Math. Phys , vol.135 , pp. 581-595
    • Zheng, Y.1
  • 31
    • 85027609246 scopus 로고
    • Master’s thesis, Institute of Mathematics, Academia Sinica
    • Yong Ouyang, Master’s thesis, Institute of Mathematics, Academia Sinica, 1993.
    • (1993)
    • Ouyang, Y.1
  • 32
  • 33
    • 0000677090 scopus 로고
    • The MmB difference solutions of 2-D Riemann problems for a 2x2 hyperbolic system of conservation laws
    • Shuli Yang and Tong Zhang, The MmB difference solutions of 2-D Riemann problems for a 2x2 hyperbolic system of conservation laws, IMP A CT of Comp. Science Enein. 3 (1991), 146-180.
    • (1991) IMP a CT of Comp. Science Enein , vol.3 , pp. 146-180
    • Yang, S.1    Zhang, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.