Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

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

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] 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 MR 0481581
  • [2] C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26, 1097-1119 (1977) MR 0457947
  • [3] 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 MR 580309
  • [4] C. M. Dafermos, Regularity and large time behavior of solutions of a conservation law without convexity, Proc. Roy. Soc. Edinburgh 99A, 201-239 (1985) MR 785530
  • [5] 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 MR 725517
  • [6] C. M. Dafermos, Generalized characteristics in hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 107, 127-155 (1989) MR 996908
  • [7] R. J. Diperna, Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws, Indiana Univ. Math. J. 24, 1047-1071 (1975) MR 0410110
  • [8] 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)) MR 0114016
  • [9] 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) MR 0320488
  • [10] 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)) MR 0267257
  • [11] P. D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10, 537-566 (1957) MR 0093653
  • [12] 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) MR 0450802
  • [13] 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 MR 2637669
  • [14] A. I. Vol'pert, The space BV and quasilinear equations, Mat. Sbornik 73 (1967) (English translation: Math. USSR-Sbornik 2, 225-267 (1967))

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35B40, 35B10, 35L65

Retrieve articles in all journals with MSC: 35B40, 35B10, 35L65


Additional Information

DOI: https://doi.org/10.1090/qam/1079918
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society