Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 

 

Asymptotic formulas for the shock wave of the scalar conservation law with smooth initial data


Author: Kazumi Tanuma
Journal: Quart. Appl. Math. 50 (1992), 109-128
MSC: Primary 35L67; Secondary 35L65, 76L05
DOI: https://doi.org/10.1090/qam/1146627
MathSciNet review: MR1146627
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] M. S. Berger and L. E. Fraenkel, On singular perturbations of nonlinear operator equations, Indiana Univ. Math. J. 20 (1970/1971), 623–631. MR 0271779, https://doi.org/10.1512/iumj.1971.20.20050
  • [2] C. M. Dafermos, Characteristics in hyperbolic conservation laws. A study of the structure and the asymptotic behaviour of solutions, Nonlinear analysis and mechanics: Heriot-Watt Symposium (Edinburgh, 1976), Vol. I, Pitman, London, 1977, pp. 1–58. Res. Notes in Math., No. 17. MR 0481581
  • [3] John Guckenheimer, Solving a single conservation law, Dynamical systems—Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E. C. Zeeman on his fiftieth birthday), Springer, Berlin, 1975, pp. 108–134. Lecture Notes in Math., Vol. 468. MR 0606765
  • [4] P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 0093653, https://doi.org/10.1002/cpa.3160100406
  • [5] Peter D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 11. MR 0350216
  • [6] David G. Schaeffer, A regularity theorem for conservation laws, Advances in Math. 11 (1973), 368–386. MR 0326178, https://doi.org/10.1016/0001-8708(73)90018-2
  • [7] Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
  • [8] G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0483954

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35L67, 35L65, 76L05

Retrieve articles in all journals with MSC: 35L67, 35L65, 76L05


Additional Information

DOI: https://doi.org/10.1090/qam/1146627
Article copyright: © Copyright 1992 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website