A dissipative logarithmic type evolution of second order in time
Analysis of PDEs
2025-05-12 v1
Abstract
In this paper, we introduce a logarithmic-type second-order model with a non-local logarithmic damping mechanism in . We present a motivation with a spectral approach to consider the equation, we consider the Cauchy problem associated with the model. More precisely, we study the asymptotic behavior of solutions as goes to infinity in -sense; namely, we prove results on the asymptotic profile and optimal decay of solutions as time goes to infinity in -sense.
Cite
@article{arxiv.2505.06214,
title = {A dissipative logarithmic type evolution of second order in time},
author = {Fábio L. Oliveira and Diego G. Santos and Maria J. M. Silva and Dennys J. C. Silva},
journal= {arXiv preprint arXiv:2505.06214},
year = {2025}
}