A dissipative logarithmic type evolution of second order in time
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915279587508224 |
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| author | Oliveira, Fábio L. Santos, Diego G. Silva, Maria J. M. Silva, Dennys J. C. |
| author_facet | Oliveira, Fábio L. Santos, Diego G. Silva, Maria J. M. Silva, Dennys J. C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A dissipative logarithmic type evolution of second order in time Oliveira, Fábio L. Santos, Diego G. Silva, Maria J. M. Silva, Dennys J. C. Analysis of PDEs 35L05, 35B40, 35C20, 35S05 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. |
| title | A dissipative logarithmic type evolution of second order in time |
| topic | Analysis of PDEs 35L05, 35B40, 35C20, 35S05 |
| url | https://arxiv.org/abs/2505.06214 |