Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Conservation laws with sharp inhomogeneities


Author: William K. Lyons
Journal: Quart. Appl. Math. 40 (1983), 385-393
MSC: Primary 35L65; Secondary 76L05
DOI: https://doi.org/10.1090/qam/693874
MathSciNet review: 693874
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  • [1] C. M. Dafermos, The entropy rate admissibility criterion for solutions of hyperbolic conservation laws, J. Diff. Eq. 14, 202-212 (1973) MR 0328368
  • [2] C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Ind. Univ. Math. J. 26, (1977) MR 0457947
  • [3] C. M. Dafermos, Characteristics in hyperbolic conservation laws: a study of the structure and asymptotic behavior of solutions, in Nonlinear analysis and mechanics 1, ed. R. J. Knops, Pitman, 1977 MR 0481581
  • [4] R. J. DiPerna, Global solutions to a class of nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 26, 1-28 (1973) MR 0330788
  • [5] R. J. DiPerna, Uniqueness of solutions to hyperbolic conservation laws, Ind. Univ. Math. 28, 137-188 (1979) MR 523630
  • [6] A. F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sbornik (N.S.) 51 (93), 99-128 (1960) MR 0114016
  • [7] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18, 697-715 (1965) MR 0194770
  • [8] J. Glimm and P. D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Mem. Amer. Math. Soc. 101 (1970) MR 0265767
  • [9] E. Hopf, The partial differential equation $ {u_t} + u{u_x} = \mu {u_{xx}}$ Comm. Pure Appl. Math. 3, 201-230 (1950) MR 0047234
  • [10] E. Hopf, On the right weak solution of the Cauchy problem for a quasilinear equation of first order, J. Math. Mech. 19, 483-487 (1969) MR 0251357
  • [11] A. Jeffrey, Quasilinear hyperbolic systems and waves, Pitman, 1976 MR 0417585
  • [12] S. N. Kružkov, First order quasilinear equations in several independent variables, Mat. Sbornik (N.S.) 81 (123) 228-255 (1970. English translation: Math. USSR-Sbornik 10, 217-243 (1970)
  • [13] P. D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10, 537-566 (1957) MR 0093653
  • [14] P. D. Lax, Shock waves and entropy, in Contributions to nonlinear functional analysis, ed. E. A. Zarantonello, pp. 603-634, New York, Academic Press, 1971 MR 0367471
  • [15] P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shcok waves, Conference Board of the Mathematical Sciences, Monograph No. 11, SIAM, 1973 MR 0350216
  • [16] T. -P. Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc. 213, 375-382 (1975) MR 0380135
  • [17] T. -P. Liu, Initial-boundary value problems for gas dynamics, Arch. Rational Mech. Anal. 64, 137-168 (1977) MR 0433017
  • [18] W. K. Lyons, The single conservation law of discontinuous media, Ph.D. Thesis, Brown Univ., 1980 MR 2631144
  • [19] T. Nishida, Global solutions for an initial boundary value problem of a quasilinear hyperbolic system, Proc. Japan Acad. 44, 642-646 (1968) MR 0236526
  • [20] O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk (N.S.) 12, 3-73 (1957) MR 0094541
  • [21] O. A. Oleinik, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation, Uspekhi Mat. Nauk (N.S.) 14, 165--70 (1959) MR 0117408
  • [22] A. I. Vol'pert, The spaces BV and quasilinear equations, Math USSP Sb2, 225-267 (1967) MR 0216338

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DOI: https://doi.org/10.1090/qam/693874
Article copyright: © Copyright 1983 American Mathematical Society

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