Abstract
We study a problem of linear viscoelasticity for the case where the relation between the Cauchy stress and strain tensors is described by a linear integral relation. Theorems on the existence and uniqueness of a solution of the problem are proved.
Similar content being viewed by others
REFERENCES
G. Fichera, “Avere una memoria tenace crea gravi problemi,” Arch. Rat. Mech. Anal., 70, 101–112 (1979).
B. D. Coleman and W. Noll, “Foundations of linear viscoelasticity,” Rev. Modern Phys., 33, 239–249 (1961).
G. Fichera, “Sul principio della memoria evanescente,” Rend. Mat. Univ. Padova., 68, 245–259 (1982).
G. Fichera, “Problemi analitici nuovi nella Fisica Matematica classica,” in: Quad. G.N.F.M., C.N.R (1984).
M. Fabrizio, “An existence and uniqueness theorem in quasistatic viscoelasticity,” Quart. J. Mech. Appl. Math., 47, No.1, 1–8 (1989).
G. Fichera, “Existence theorem in elasticity,” in: Handbuch der Physik, Vol. VIa/2, Springer, Heidelberg, (1972), pp. 347–389.
F. Treves, Basic Linear Partial Differential Equations, Academic Press, New York (1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Matarazzo, G. Time-Irreversibility and Existence and Uniqueness of Solutions of Problems in Linear Viscoelasticity. Ukrainian Mathematical Journal 52, 1058–1067 (2000). https://doi.org/10.1023/A:1005225632662
Issue Date:
DOI: https://doi.org/10.1023/A:1005225632662