This is a preview of subscription content, log in via an institution to check access.
References
Brio, M., & C. C. Wu: Characteristic fields for the equations of magnetohydrodynamics, in Non-strictly hyperbolic conservation laws, Proc. of an AMS special session, held January 9–10, 1985, Contemporary Mathematics, vol. 60 (1987), 19–23.
Courant, R., & K. O. Friedrichs: Supersonic flow and shockwaves, New York (1948).
Dafermos, C. M.: The equations of elasticity are special, in Trends in Applications of pure mathematics to mechanics, vol. III, ed. R. J. Knops, London (1981), 96–103.
Dafermos, C. M.: Quasilinear hyperbolic systems with involutions, Arch. Rational Mech. Anal. 94 (1986), 373–389.
DiPerna, R.: Singularities of solutions of nonlinear hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 52 (1973), 244–257.
Freistühler, H.: Anomale Schocks, strukturell labile Lösungen und die Geometrie der Rankine-Hugoniot-Bedingungen, Doctoral Thesis, Bochum (1987).
Glimm, J.: Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 95–105.
Gogosov, V. V.: Resolution of an arbitrary discontinuity in magnetohydrodynamics, J. Appl. Math. Mech. 25 (1961), 148–170.
Isaacson, E., Marchesin, D., Plohr, B., & B. Temple: The classification of quadratic Riemann problems (I), Madison Research Center Rep. No. 2891 (1986).
Jackson, J. D.: Classical Electrodynamics, New York (1975).
Jeffrey, A., & T. Taniuti: Nonlinear wave propagation, New York (1964).
John, F.: Formation of singularities in one-dimensional wave propagation, Comm. Pure Appl. Math. 27 (1974), 377–405.
Keyfitz, B. L.: A survey of nonstrictly hyperbolic conservation laws, in: Nonlinear hyperbolic systems, Proc. 1st Int. Conf. on Hyperbolic Problems held at St. Etienne 1986 (1987), 152–162.
Keyfitz, B., & H. Kranzer: A system of non-strictly hyperbolic conservation laws arising in elasticity theory, Arch. Rational Mech. Anal. 72 (1980), 219–241.
Lax, P.: Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10 (1957), 537–566.
Liu, T.-P.: The Riemann problem for general systems of conservation laws, J. Diff. Eqs. 18 (1975), 218–234.
Liu, T.-P.: Admissible solutions of hyperbolic conservation laws, AMS Mem. No. 240 (1981).
Liu, T.-P., & C.-H. Wang: On a non-strictly hyperbolic system of conservation laws, J. Diff. Eqs. 57 (1985), 1–14.
Majda, A.: Stability of multidimensional shockfronts, AMS Mem. No. 275 (1983).
Temple, B.: Global solution of the Cauchy problem for a class of 2×2 nonstrictly hyperbolic conservation laws, Adv. Appl. Math. 3 (1982), 335–375.
Truesdell, C. A., & W. Noll: The nonlinear field theories of mechanics, in Handbuch der Physik, S. flügge (ed.), vol. III/3, Berlin (1965).
Schaeffer, D. G., & M. Shearer: Classification of 2×2-systems of non-strictly hyperbolic conservation laws, with applications to oil recovery, Comm. Pure Appl. Math. 40 (1987), 141–178.
Schaeffer, D. G., Shearer, M., Marchesin, D., & P. Paes-Leme: Solution of the Riemann problem for a prototype system of non-strictly hyperbolic conservation laws, Arch. Rational Mech. Anal. 97 (1987), 299–320.
Shearer, M.: The Riemann problem for the planar motion of an elastic string, J. Diff. Eqs. 61 (1986), 149–163.
Author information
Authors and Affiliations
Additional information
Communicated by C. Dafermos
Rights and permissions
About this article
Cite this article
Freistühler, H. Rotational degeneracy of hyperbolic systems of conservation laws. Arch. Rational Mech. Anal. 113, 39–64 (1991). https://doi.org/10.1007/BF00380815
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00380815