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An abstract Volterra equation with applications to linear viscoelasticity. (English) Zbl 0212.45302


MSC:

45D05 Volterra integral equations
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
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[1] Edelstein, W. S.; Gurtin, M. E., Arch. Ration. Mech. Anal., 17, 47-60 (1964)
[2] Odeh, F.; Tadjbakhsh, I., Arch. Ration. Mech. Anal., 18, 244-250 (1965)
[3] Levin, J. J., J. Differential Equations, 4, 176-186 (1968)
[4] Lions, J. L.; Magenes, E., (Problèmes aux Limites non Homogènes, Vol. 1 (1968), Dunod: Dunod Paris) · Zbl 0165.10801
[5] Lions, J. L., Équations Différentielles-Opérationnelles et problèmes aux limites (1961), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0098.31101
[6] Hartman, P., Ordinary Differential Equations (1964), Wiley: Wiley New York · Zbl 0125.32102
[7] Levin, J. J., (Proc. Amer. Math. Soc., 14 (1963)), 534-541
[8] Levin, J. J.; Nohel, J. A., Mich. Math. J., 12, 431-447 (1965)
[9] Corduneanu, C., Compt. Rend. Acad. Sci. Paris, 256, 3564-3567 (1963)
[10] Halanay, A., J. Math. Anal. Appl., 10, 319-324 (1965)
[11] Friedman, A., J. Analyse Math., 11, 381-413 (1963)
[12] Volterra, V., J. Math. Pures Appl., 7, 249-298 (1928)
[13] Edelstein, W. S., Arch. Ration. Mech. Anal., 22, 121-128 (1966)
[14] Friedman, A.; Shinbrot, M., Trans. Amer. Math. Soc., 126, 131-179 (1967)
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