This is a preview of subscription content, log in via an institution to check access.
References
Courant, R., & K. O. Friedrichs, Supersonic Flow and Shock Waves. New York: Interscience-Wiley 1948.
Lax, P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7, 159–193 (1954);
Lax, P. D. Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math. 10, 537–566 (1957);
Lax, P. D. Initial value problems for nonlinear hyperbolic equations. Conference on Partial Differential Equations, University of Kansas, TR 14 (1954), pp. 13–57.
Jeffrey, A., & T. Taniuti, Nonlinear Wave Propagation. New York: Academic Press 1964.
Bazer, J., & F. Karal, Simple wave motion in magnetoelasticity. Geophys. J. R. Astr. Soc. 25, 127–156 (1971).
Bazer, J., & W. B. Ericson, Hydromagnetic shocks. Astrophys. J. 129, 758–785 (1959).
Alfvén, H., Cosmical Electrodynamics. Oxford: Clarendon Press 1950.
Paria, G., Magnetoelasticity and magneto-thermoelasticity. Advances in Applied Mechanics 10, 78–112 (1967).
Knopoff, L., The interaction between elastic wave motions and a magnetic field in electrical conductors. J. Geophys. Research 60, 441–456 (1955).
Baños, A., Jr., Normal modes characterizing magneto-elastic plane waves. Phys. Rev. 104, 300–305 (1956).
Chadwick, P., Elastic waves propagated in a magnetic field. International Congress Mech. Appl., Brussels VII (1956/57).
Nardini, R., Sui fronti d'onda nella magnetoelasticitá. Rend. Sem. Mat. Univ. Padova 28, 225–243 (1958).
Keilis-Borok, V. I., & A. S. Munin, Magnetoelastic waves and the boundary of the earth's core. Izv. Geophys. Ser. 1529–1541 (English translation 1960, pp. 1089–1095).
Ruderman, M., (a) Solid stars. Scientific American, Feb. 1971, pp. 22–31; (b) Superdense matter in stars. J. de Physique, C3, supplement no. 11–12. Tome 30 Nov.– Dec. (1969) C3-152-C3-160.
Bowers, R., Plasmas in solids. Scientific American, Nov. (1963), pp. 46–53.
Bowers, R., & M. C. Steele, Plasma effects in solids. Proc. IEEE, Oct. (1964), pp. 1105–1112.
Maxfield, B. W., Helicon waves in solids. Amer. J. of Physics 37, 241–269 (1969).
Bland, D. R., Nonlinear Dynamic Elasticity. Waltham, Mass.: Blaisdell Publ. Co. (1969);
Bland, D. R. Plane isentropic large displacement simple waves in a compressible elastic solid. ZAMP 16, 752–769 (1965).
Landau, L. D., & E. M. Lifshitz, Theory of Elasticity. Addison-Wesley 1959.
Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. 2. New York: Interscience-Wiley 1962.
Bazer, J., Geometrical magnetoelasticity. Geophys. J. R. astr. Soc. 25, 207–238 (1971).
Lüst, R., Magneto-hydrodynamische Stoßwellen in einem Plasma unendlicher Leitfähigkeit, Z. Naturforsch. 8a, 277–284 (1953).
Friedrichs, K. O., Nonlinear wave motion in magnetohydrodynamics. Los Alamos Sci. Lab. Report LAMS-2105 (Physics), written September 1954, distributed, March 1957. See also the somewhat emended and more available version of this report written jointly with H. Kranzer, Notes on magnetohydrodynamics, VIII, Nonlinear wave motion, AEC Computing and Applied Mathematics Center, Institute of Mathematical Sciences, New York University, Report No. NYO-6486 (1958).
Gelfand, I. M., & K. I. Babenko, Remarks on hyperbolic systems. Sci. Papers of the Colleges, Phys. and Math. Sci. 1, 12–18 (1958). Russian [Nauch. Doklady Vysshei Shkoly, Fiz. Mat. Nauki 1, 12–18 (1958)].
Karal, F., & J. Bazer, Nonlinear magnetoelastic wave motion in incompressible infinitely conducting solids. (To appear.)
Dunkin, J. W., & A. C. Eringen, On the propagation of waves in an electromagnetic elastic solid. Int. J. Engng. Sci. 1, 461–495 (1967).
Kaliski, S., Propagation of nonlinear loading waves in a magnetic field for a perfect conductor. Proc. Vibr. Probl. 1 (5), 11–26 (1960);
Kaliski, S. Plane shock waves in solids with perfect electrical conductivity in a magnetic field. Proc. Vibr. Prob. 2 (1), 57–66 (1961).
Bazer, J., Resolution of an initial shear flow discontinuity. Astrophys. J. 128, 686–721 (1958).
Truesdell, C., & R. A. Toupin, The Classical Field Theories. Handbuch der Physik, pp. 226–793. New York: Springer 1960.
Truesdell, C., & W. Noll, The Nonlinear Field Theories of Mechanics. Handbuch der Physik, pp. 1–602. New York: Springer 1965.
Prager, W., Introduction to Mechanics of Continua. Boston: Ginn and Co. 1961.
Tiersten, H. F., Coupled magnetomechanical equations for magnetically saturated insulators. J. Math. Phys. 5, 1298 (1964).
Toupin, R. A., A dynamical theory of elastic dialectrics. Intern. J. Eng. Sci. 1, 101–126 (1963).
Stratton, J. A., Electromagnetic Theory. New York: McGraw-Hill 1941.
Kanwal, R. P., & C. Truesdell, Electric current and fluid spin created by the passage of a magnetosonic wave, Phys. Fluids 5, 442–449 (1962);
Kanwal, R. P., & C. Truesdell Fluid and magnetic distortion carried by magnetosonic waves. Phys. Fluids 5, 368–369 (1962).
Lundquist, S., Studies in magneto-hydrodynamics. Arkiv Fysik 5, 297–347 (1952).
Lilley, F. E. M., & D. E. Smiley, Elastic wave motion and a nonuniform magnetic field in electrical conductors. J. Geophys. Res. 73, 6527–6533 (1968).
Green, A. E., & J. E. Adkins, Large Elastic Deformations. Oxford: Clarendon Press 1970.
Author information
Authors and Affiliations
Additional information
Communicated by S. Antman
Rights and permissions
About this article
Cite this article
Bazer, J., Ericson, W.B. Nonlinear wave motion in magnetoelasticity. Arch. Rational Mech. Anal. 55, 124–192 (1974). https://doi.org/10.1007/BF00249935
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00249935