C. M. Dafermos and J. A. Nohel; A nonlinear hyperbolic Volterra equation in Viscoelasticity. Amer. J. Math Supplement (1981) 87-116. Home/Search Document Not in Database Summary Related Articles Check |
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Uniform Rates of Decay in Nonlinear Viscoelasticity for.. - Rivera, Barreto (1996) (2 citations) (Correct)
....where oe denotes the stress tensor, u the displacement and g the relaxation function. In this direction we have a large literature about existence of classical solution (see for example [5] Partially supported by a grant of CNPq BRASIL y Partially supported by a grant of CNPq BRASIL 1 [6] [7], 12] 16] 10] 11] among others) when the inital data is small in H 3 norm. The asumption the authors consider, about the relaxation function, in above references implies that the relaxation decays to zero as time goes to infinity, without rate of decay. Under this condition they showed, ....
....is given by oe(x; t) Z 1 0 (t Gamma ; u x (x; u x (x; t) d: In this general condition the relaxation function is given by: g(t) Gamma u x ( Delta; t; 0; 0) 1. 1) Our decay and existence result improves others obtained in nonlinear viscoelastic equations (see [5] 6] [7], 10] 11] 12] 16] 14] among others) The equation for the displacement u reads as follows u tt = Z t Gamma1 f (t Gamma ; u x ( Delta; u x ( Delta; t) g x d (1.2) with null history (for simplicity) u = 0; 8t 0; 1.3) 2 with initial condition u(x; 0 ) u 0 (x) u t (x; 0 ) u ....
[Article contains additional citation context not shown here]
C. M. Dafermos and J. A. Nohel; A nonlinear hyperbolic Volterra equation in Viscoelasticity. Amer. J. Math Supplement (1981) 87-116.
Decay rates for Viscoelastic plates with memory - Rivera, Lapa, Barreto (Correct)
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C. M. Dafermos and J. A. Nohel; A nonlinear hyperbolic Volterra equation in Viscoelasticity. Amer. J. Math Supplement (1981) 87-116.
Smoothing effect and propagations of singularities for.. - Rivera, Fatori (Correct)
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C. M. Dafermos and J. A. Nohel; A nonlinear hyperbolic Volterra equation in Viscoelasticity. Amer. J. Math Supplement (1981) 87-116.
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