L2 asymptotic profiles of solutions to linear damped wave equations

In this paper we obtain higher order asymptotic expansions of solutions to the Cauchy problem of the linear damped wave equation in R-n u(tt) - Delta u + u(t) = 0, u(0, x) = u0(x), ut (0, x) = u(1)(x), where n is an element of N and u(0), u(1) is an element of L-1(R-n) boolean AND L-2(R-n). Established hyperbolic effects seem to be new in the sense that the order of obtained expansions depends on the spatial dimension. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we obtain higher order asymptotic expansions of solutions to the linear damped wave equation Cauchy problem, where the order of expansions depends on the spatial dimension, presenting new hyperbolic effects.