English

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 RNR^N. 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 tt goes to infinity in L2L^2-sense; namely, we prove results on the asymptotic profile and optimal decay of solutions as time goes to infinity in L2L^2-sense.

Keywords

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}
}
R2 v1 2026-06-28T23:27:31.099Z