J. M. Greenberg; A priori estimates for flows in dissipative materials. J. Math Anal. Appl. 60, (1977) 617-630 Home/Search Document Not in Database Summary Related Articles Check |
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Decay rates for Viscoelastic plates with memory - Rivera, Lapa, Barreto (Correct)
....nonlinear one dimensional viscoelastic equation as we can verify in [1, 4, 9, 10] provided the initial data is small enough. Also it was shown that solutions decays to zero; but no rate of decay was obtained. Concerning uniform rate of decay of the solutions, we have first the work of Greenberg [7] who proved, in the particular case when the relaxation function is an exponential of the form g(t) e Gammat , that the solution of the nonlinear viscoelastic equation decays exponentially to zero as time goes to infinity. The method is based on the fact that the viscoelastic equation is ....
J. M. Greenberg; A priori estimates for flows in dissipative materials. J. Math Anal. Appl. 60, (1977) 617-630
Uniform Rates of Decay in Nonlinear Viscoelasticity for.. - Rivera, Barreto (1996) (2 citations) (Correct)
....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, among other ....
....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 1 (x) ....
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J. M. Greenberg; A priori estimates for flows in dissipative materials. J. Math Anal. Appl. 60, (1977) 617-630
Smoothing effect and propagations of singularities for.. - Rivera, Fatori (Correct)
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J. M. Greenberg; A priori estimates for flows in dissipative materials. J. Math Anal. Appl. 60, (1977) 617-630
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