Asymptotic profiles for a wave equation with parameter dependent logarithmic damping
Analysis of PDEs
2021-12-01 v1 Mathematical Physics
math.MP
Abstract
We study a nonlocal wave equation with logarithmic damping which is rather weak in the low frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in the whole space and we study the asymptotic profile and optimal estimates of the solutions and the total energy as time goes to infinity in L^{2}-sense. In that case some results on hypergeometric functions are useful.
Cite
@article{arxiv.2009.06395,
title = {Asymptotic profiles for a wave equation with parameter dependent logarithmic damping},
author = {Ruy Coimbra Charao and Marcello D'Abbicco and Ryo Ikehata},
journal= {arXiv preprint arXiv:2009.06395},
year = {2021}
}
Comments
20 pages. arXiv admin note: text overlap with arXiv:2002.06319