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arXiv · 2505.06214

A dissipative logarithmic type evolution of second order in time

Fábio L. Oliveira·Diego G. Santos·Maria J. M. Silva·Dennys J. C. Silva
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Abstract

In this paper, we introduce a logarithmic-type second-order model with a non-local logarithmic damping mechanism in $R^N$. 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 $t$ goes to infinity in $L^2$-sense; namely, we prove results on the asymptotic profile and optimal decay of solutions as time goes to infinity in $L^2$-sense.

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Fábio L. Oliveira, Diego G. Santos, Maria J. M. Silva, Dennys J. C. Silva. 2025-05-09. A dissipative logarithmic type evolution of second order in time. https://arxiv.org/abs/2505.06214

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