L2 asymptotic profiles of solutions to linear damped wave equations

[摘要] 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.

[发布日期] 2021-09-25

[关键词] Damped wave equation;Asymptotic expansion;Diffusion phenomenon;Wave effect