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Some stability theorems for an abstract equation in Hilbert space with applications to linear elastodynamics. (English) Zbl 0378.35059

MSC:
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
34G99 Differential equations in abstract spaces
74H55 Stability of dynamical problems in solid mechanics
74B99 Elastic materials
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References:
[1] Knops, R.J; Payne, L.E, Continuous data dependence for the equations of classical elastodynamics, (), 481-491 · Zbl 0184.51004
[2] Levine, H.A, Logarithmic convexity and the Cauchy problem for some abstract second order differential inequalities, J. differential equations, 8, 34-55, (1970) · Zbl 0194.13101
[3] Wang, C.C, On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations, Arch. rational mech. anal., 27, 33-92, (1967) · Zbl 0187.48802
[4] Bloom, F; Wang, C.C, Material uniformity and inhomogeneity in anelastic bodies, Arch. rational mech. anal., 53, 246-276, (1974) · Zbl 0317.73066
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