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Growth estimates for solutions to initial-boundary value problems in viscoelasticity. (English) Zbl 0361.45010

MSC:
45K05 Integro-partial differential 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] Dafermos, C.M, An abstract Volterra equation with applications to linear viscoelasticity, J. differential equations, 7, 554-569, (1970) · Zbl 0212.45302
[2] Bloom, F, Continuous data dependence for an abstract Volterra integrodifferential equation in Hilbert space with applications to viscoelasticity, Annali Della scuola normale (Pisa) (classe di scienze), IV, 179-207, (1977) · Zbl 0342.45014
[3] Knops, R.J; Payne, L.E, Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics, Arch. rat. mech. anal., 41, 363-398, (1971) · Zbl 0227.35017
[4] Levine, H.A, Uniqueness and growth of weak solutions to certain linear differential equations in Hilbert space, J. differential equations, 17, 73-81, (1975) · Zbl 0294.34044
[5] John, F, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. pure appl. math., 13, 551-585, (1960) · Zbl 0097.08101
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