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
Full-text PDF Free Access
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C. M. Dafermos, The entropy rate admissibility criterion for solutions of hyperbolic conservation laws, J. Diff. Eq. 14, 202–212 (1973)
C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Ind. Univ. Math. J. 26, (1977)
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
R. J. DiPerna, Global solutions to a class of nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 26, 1–28 (1973)
R. J. DiPerna, Uniqueness of solutions to hyperbolic conservation laws, Ind. Univ. Math. 28, 137–188 (1979)
A. F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sbornik (N.S.) 51 (93), 99–128 (1960)
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18, 697–715 (1965)
J. Glimm and P. D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Mem. Amer. Math. Soc. 101 (1970)
E. Hopf, The partial differential equation ${u_t} + u{u_x} = \mu {u_{xx}}$ Comm. Pure Appl. Math. 3, 201–230 (1950)
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)
A. Jeffrey, Quasilinear hyperbolic systems and waves, Pitman, 1976
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)
P. D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10, 537–566 (1957)
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
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
T. -P. Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc. 213, 375–382 (1975)
T. -P. Liu, Initial-boundary value problems for gas dynamics, Arch. Rational Mech. Anal. 64, 137–168 (1977)
W. K. Lyons, The single conservation law of discontinuous media, Ph.D. Thesis, Brown Univ., 1980
T. Nishida, Global solutions for an initial boundary value problem of a quasilinear hyperbolic system, Proc. Japan Acad. 44, 642–646 (1968)
O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk (N.S.) 12, 3–73 (1957)
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)
A. I. Vol’pert, The spaces BV and quasilinear equations, Math USSP Sb2, 225–267 (1967)
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© Copyright 1983
American Mathematical Society
