Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term. (June 2022) - Kagei, Yoshiyuki; Takeda, Hiroshi
Abstract: The Cauchy problem for a nonlinear elastic wave equation 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 → ∞ are also derived.