Uniform Rates of Decay in Anisotropic Thermo-Viscoelasticity
- 30 Downloads
We consider the anisotropic and inhomogeneous thermo-viscoelastic equation. We prove that the first and second-order energy decay exponentially as time goes to infinity provided the relaxation function also decays exponentially to zero. While if the relaxation functions decay polynomially to zero, then the energy decays also polynomially. That is, the kernel of the convolution defines the rate of decay of the solution.
Unable to display preview. Download preview PDF.
- 1.MacCamy, R. C.: A model for one dimensional nonlinear viscoelasticity, Quart. Appl. Math. 35(1977), 21-33.Google Scholar
- 2.Dafermos, C. M.: On the existence and the asymptotic stability of solution to the equation of linear thermoelasticity, Arch. Rational Mech. Anal. 29(1968), 241-271.Google Scholar
- 3.Dafermos, C. M.: An abstract Volterra equation with application to linear viscoelasticity, J. Differential Equations 7(1970), 554-569.Google Scholar
- 4.Dafermos, C. M.: Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37(1970), 297-308.Google Scholar
- 5.Dassios, G. and Zafiropoulos, F.: Equipartition of energy in linearized 3-D viscoelasticity, Quart. Appl. Math. 48(4) (1990), 715-730.Google Scholar
- 6.Kim, J. U.: On the energy decay of a linear thermoelastic bar and plate, SIAM J. Math. Anal. 23(1992), 889-899.Google Scholar
- 7.Muñoz Rivera, J. E.: Energy decay rates in linear thermoelasticity, Funkcial. Ekvac. 35(1992), 19-30.Google Scholar
- 8.Muñoz Rivera, J. E.: Asymptotic behaviour in linear viscoelasticity, Quart. Appl. Math. III(4) (1994), 629-648.Google Scholar
- 9.Pereira, D. C. and Menzala, G. P.: Exponential decay of solutions to a coupled system of equations of linear thermoelasticity, Comput. Appl. Math. 8(1989), 193-204.Google Scholar
- 10.Racke, R. and Shibata, Y.: Global smooth solution and asymptotic stability in one dimensional nonlinear thermoelasticity, Arch. Rational Mech. Anal. 116(1991), 1-34.Google Scholar
- 11.Racke, R., Shibata, Y. and Zheng, S.: Global solvability and exponential stability in one dimensional nonlinear thermoelasticity, Quart. Appl. Math. 51(1993), 751-763.Google Scholar