Convergence to diffusion waves of solutions to nonlinear viscoelastic model with fading memory
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We study the large time behavior inL2 of solutions to a model for the motion of an unbounded, homogeneous, viscoelastic bar with fading memory. Decay rates for the solutions are obtained under the assumption that the initial data and histories are smooth and small. Moreover, convergence of the solutions to diffusion waves, which are solutions of Burgers equations, is proved and rates are obtained. Our method is based on the study of properties of the solutions to the linearized system in the Fourier space.
KeywordsNeural Network Fourier Statistical Physic Complex System Initial Data
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