References
Coleman, B. D., & M. E. Gurtin, Waves in materials with memory, II. On the growth and decay of one-dimensional acceleration waves. Arch. Rational Mech. Anal. 19 (1965), 266–298.
Coleman, B. D., & W. Noll, An approximation theorem for functionals with applications in continuum mechanics. Arch. Rational Mech. Anal. 6 (1960), 355–370.
Dafermos, C. M., Dissipation in materials with memory. Proc. Symp. on Viscoelasticity and Rheology held at the MRC, Univ. of Wisconsin, 1984. To be published by Academic Press.
Dafermos, C. M., & L. Hsiao, Development of singularities in solutions of the equations of nonlinear thermoelasticity. Quart. Appl. Math. (to appear).
Dafermos, C. M., & J. A. Nohel, A nonlinear hyperbolic Volterra equation in viscoelasticity. Am. J. Math. Suppl. dedicated to P. Hartman (1981), 87–116.
Hattori, H., Breakdown of smooth solutions in dissipative nonlinear hyperbolic equations. Quart. Appl. Math. 40 (1982), 113–127.
Hrusa, W. J., A nonlinear functional differential equation in Banach space with applications to materials with fading memory. Arch. Rational Mech. Anal. 84 (1983), 99–137.
Klainerman, S., & A. Majda, Formation of singularities for wave equations including the nonlinear vibrating string. Comm. Pure Appl. Math. 33 (1980), 241–263.
Lax, P. D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Physics 5 (1964), 611–613.
MacCamy, R. C., A model for one-dimensional, nonlinear viscoelasticity. Quart. Appl. Math. 35 (1977), 21–33.
MacCamy, R. C., & V. J. Mizel, Existence and nonexistence in the large of solutions of quasilinear wave equations. Arch. Rational Mech. Anal. 25 (1967), 299–320.
Malek-Madani, R., & J. A. Nohel, Formation of singularities for a conservation law with memory. SIAM J. Math. Anal. (to appear).
Noll, W., A mathematical theory for the mechanical behavior of continuous media. Arch. Rational Mech. Anal. 2 (1958/59), 197–226.
Author information
Authors and Affiliations
Additional information
Dedicated to Walter Noll on his sixtieth birthday
Rights and permissions
About this article
Cite this article
Dafermos, C.M. Development of singularities in the motion of materials with fading memory. Arch. Rational Mech. Anal. 91, 193–205 (1986). https://doi.org/10.1007/BF00250741
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00250741