Abstract
The Cauchy problem for nonlinear elastic wave equations with viscoelastic damping terms is investigated in the Lp framework. Sharp estimates of the global solutions in t for the higher order derivatives are established. The proof is based on the Gronwall type argument for 1<p<∞, the use of the difference of the propagation speed of the fundamental solutions for p=1 and the bootstrap argument for p=∞, combined with the sharp estimates for the linearized solutions.
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