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Abstract: We prove a global existence theorem for the nonlinear viscoelastic equation for small data in H 2 (]0; L[) and that the solution decays algebraically to zero when the kernel decays also algebraically as t goes to infinity. That is, if the kernel g satisfies g 0 (t) \Gammac 0 g(t) 1+ 1 p ; and g; g 1+ 1 p 2 L 1 (IR) with p ? 2; then the firts and second order energy decay as 1 (1+t) p . AMS classification code: 35B40, 35L05, 35L70 Keywords and phrases: viscoelasticity,... (Update)
Context of citations to this paper: More
...g 0 (t) g(t) the convolution term is eliminated, so the authors work with the resulting purely ordinary di erential equation. In [9, 11, 12] was proved that the rate of decay of the solution depends on the rate of decay of the relaxation function, that is if the relaxation...
...by using the theory of semigroups. For detailed discussion about the existence and regularity of a solution of viscoelastic system, we refer to [JR, RB, RL] In order to use the theory of semigroups, we write (2.10) as follows # # # # # # # # # # # # # # # # # # # # # # # # # #...
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BibTeX entry: (Update)
Mu~noz Rivera, J.E., Barreto, R.K.: Uniform rates of decay in nonlinear viscoelasticity for polynomial decaying kernels. Applicable Analysis 60 (1996), 341-357. http://citeseer.ist.psu.edu/rivera96uniform.html More
@misc{ rivera96uniform,
author = "M. Rivera and J. Barreto",
title = "Uniform rates of decay in nonlinear viscoelasticity for polynomial decaying
kernels",
text = "Mu~noz Rivera, J.E., Barreto, R.K.: Uniform rates of decay in nonlinear
viscoelasticity for polynomial decaying kernels. Applicable Analysis 60
(1996), 341-357.",
year = "1996",
url = "citeseer.ist.psu.edu/rivera96uniform.html" }
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15 An Abstract Volterra Equation with application to linear Vis.. (context) - Dafermos
9 the energy decay of a linear thermoelastic bar and plate (context) - Kim - 1992
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7 Energy decay rates in linear thermoelasticity (context) - noz - 1992
5 the asymptotic partition of the energy in linear thermoelast.. (context) - Chirita - 1987
4 Dissipation rates and Partition of energy in Thermoelasticit.. (context) - Dassios, Grillakis - 1984
3 The Cauchy problem in one dimensional nonlinear Viscoelastic.. (context) - Hrusa, Nohel - 1985
3 A nonlinear hyperbolic Volterra equation in Viscoelasticity (context) - Dafermos, Nohel - 1981
3 Equipartition of energy in Linearized 3-D Viscoelasticity (context) - Dassios, Zafiropoulos - 1990
3 A model for one dimensional non linear Viscoelasticity (context) - Camy - 1977
3 Global existence and asymptotic stability for a semilinear V.. (context) - Hrusa - 1985
3 A priori estimates for flows in dissipative materials (context) - Greenberg - 1977
2 Mathematical problems in Viscoelasticity Pitman monograph in.. (context) - Renardy, Hrusa et al. - 1987
1 Energy methos for non linear hyperbolic Volterra integrodiff.. (context) - Dafermos, Nohel - 1979
1 global smooth solution and uniform rate of decay in nonlinea.. (context) - noz - 1994
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