Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term (2109.04628v3)

Abstract: The Cauchy problem for a nonlinear elastic wave equations with viscoelastic damping terms is considered on the 3 dimensional whole space. Decay and smoothing properties of the solutions are investigated when the initial data are sufficiently small; and asymptotic profiles as $t \to \infty$ are also derived.