arXiv Analytics

Sign in

arXiv:2009.06395 [math.AP]AbstractReferencesReviewsResources

Asymptotic profiles for a wave equation with parameter dependent logarithmic damping

Ruy Coimbra Charao, Marcello D'Abbicco, Ryo Ikehata

Published 2020-09-11Version 1

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.

Comments: 20 pages. arXiv admin note: text overlap with arXiv:2002.06319
Categories: math.AP, math-ph, math.MP
Subjects: 35L05, 35B40, 35B05, 35B45, 35C20, 35S05
Related articles: Most relevant | Search more
arXiv:2010.02485 [math.AP] (Published 2020-10-06)
A dissiptive logarithmic type evolution equation: asymptotic profile and optimal estimates
arXiv:2104.08468 [math.AP] (Published 2021-04-17)
A dissipative logarithmic-Laplacian type of plate equation: Asymptotic profile and decay rates
arXiv:2209.10154 [math.AP] (Published 2022-09-21)
Asymptotic profile of L^2-norm of solutions for wave equations with critical log-damping

Links

Toolbox