Asymptotic oscillations of solutions of scalar conservation laws with convexity under the action of a linear excitation
Author:
Athanasios N. Lyberopoulos
Journal:
Quart. Appl. Math. 48 (1990), 755-765
MSC:
Primary 35B40; Secondary 35B10, 35L65
DOI:
https://doi.org/10.1090/qam/1079918
MathSciNet review:
MR1079918
Full-text PDF Free Access
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- C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26 (1977), no. 6, 1097–1119. MR 457947, DOI https://doi.org/10.1512/iumj.1977.26.26088
- C. M. Dafermos, Asymptotic behavior of solutions of hyperbolic balance laws, Bifurcation phenomena in mathematical physics and related topics (Proc. NATO Advanced Study Inst., Cargèse, 1979) NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 54, Reidel, Dordrecht-Boston, Mass., 1980, pp. 521–533. MR 580309
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A. I. Vol’pert, The space BV and quasilinear equations, Mat. Sbornik 73 (1967) (English translation: Math. USSR-Sbornik 2, 225–267 (1967))
C. M. Dafermos, Characteristics in hyperbolic conservation laws, Nonlinear Analysis and Mechanics (R.J. Knops, Ed.), Research Notes in Math. No. 17, Pitman, London, 1977, pp. 1–58
C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26, 1097–1119 (1977)
C. M. Dafermos, Asymptotic behavior of solutions of hyperbolic balance laws, Bifurcation Phenomena in Mathematical Physics (C. Bardos and D. Bessis, Eds.), D. Reidel, Dordrecht, 1979, pp. 521–533
C. M. Dafermos, Regularity and large time behavior of solutions of a conservation law without convexity, Proc. Roy. Soc. Edinburgh 99A, 201–239 (1985)
C. M. Dafermos, Hyperbolic systems of conservation laws, Systems of Nonlinear Partial Differential Equations (J.M. Ball, Ed.), NATO ASI Series C No. 111, D. Reidel, Dordrecht, 1983, pp. 25–70
C. M. Dafermos, Generalized characteristics in hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 107, 127–155 (1989)
R. J. Diperna, Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws, Indiana Univ. Math. J. 24, 1047–1071 (1975)
A. F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sbornik (N.S.) 51, 99–128 (1960) (English translation: Amer. Math. Soc. Transl. Ser. 2 42, 199–231 (1964))
J. M. Greenberg and D. D. Tong, Decay of periodic solutions of $\partial u/\partial t + \partial f\left ( u \right )/\partial x = 0$, J. Math. Anal. Appl. 43, 56–71 (1973)
S. N. Kružkov, First order quasilinear equations in several independent variables, Mat. Sbornik (N.S.) 81, 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)
T.-P. Liu, Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws, Comm. Pure Appl. Math. 30, 585–610 (1977)
A. N. Lyberopoulos, Asymptotic oscillations of solutions of scalar conservation laws with or without convexity under the action of a linear excitation, Ph.D. dissertation, Brown University, 1989
A. I. Vol’pert, The space BV and quasilinear equations, Mat. Sbornik 73 (1967) (English translation: Math. USSR-Sbornik 2, 225–267 (1967))
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© Copyright 1990
American Mathematical Society
