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Decay estimates for the generalized damped extensible string and beam equation. (English) Zbl 0524.35026


MSC:

35G25 Initial value problems for nonlinear higher-order PDEs
34G20 Nonlinear differential equations in abstract spaces
35B40 Asymptotic behavior of solutions to PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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References:

[1] Ball, J. M., Saddle point analysis for an ordinary differential equation in a Banach space and an application to dynamic buckling of a beam, (Dickey, R. W., Proc. Symp. Nonlinear Elasticity (1973), Academic Press: Academic Press New York), 93-160 · Zbl 0288.34057
[2] Brito, E. H., The damped elastic stretched string equation generalized: existence, uniqueness, regularity and stability, Applicable Analysis, 13, 219-233 (1982) · Zbl 0458.35065
[3] Brito, E. H., A nonlinear hyperbolic equation, Int. J. Math. math. Sci., 3, 505-520 (1980) · Zbl 0444.34060
[4] Dickey, R. W., Dynamic stability of equilibrium states of the extensible beam, Proc. Am. math. Soc., 41, 94-102 (1973) · Zbl 0284.35047
[5] Lions, J. L.; Magenes, E., Problèmes aux Limites non Homogènes et Applications, Vol. 1 (1968), Dunod: Dunod Paris · Zbl 0165.10801
[6] Mikhlin, S. G., Variational Methods in Mathematical Physics (1964), Pergamon Press: Pergamon Press Oxford, (Translated by T. Boddington) · Zbl 0119.19002
[7] Nishihara, K., Exponential decay of solution for some quasilinear hyperbolic equation with linear damping (1982), Tokyo National Technical College
[8] Riesz, F.; Nagy, B. Sz, Functional Analysis (1972), Frederick Ungar: Frederick Ungar New York
[9] Timoshenko, S.; Gere, J. M., Theory of Elastic Stability (1961), McGraw-Hill: McGraw-Hill New York
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