Decay rates of solutions to thermoviscoelastic plates with memory |
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| Authors: | Rivera JEN; Barreto RK |
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| Institution: |
Z National Laboratory for Scientific Computation, Department of Research and Development, Rua Lauro Muller 455, Botafogo Cep. 22290, Rio de Janeiro, RJ, Brasil Y Institute of Mathematics, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, Brasil ZZ University Federal Fluminense, Rio de Janeiro, RJ, Brasil
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| Abstract: | We consider the thermoelastic plate under the presence of along range memory. We find uniform rates of decay (in time)of the energy, provided that suitable assumptions on the relaxationfunctions are given. Namely, if the relaxation decays exponentiallythen the first order energy also decays exponentially. Whenthe relaxation g satisfies -c1g(t)1+1/p  g'(t) -cog(t)1+1/p; and g,g1-1/p  L1 (R) withp > 2 then the energy decays as 1/(1+t)p. A new Liapunov functionalis built for this problem. |
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