{
  "id": "2505.06214",
  "version": "v1",
  "published": "2025-05-09T17:44:01.000Z",
  "updated": "2025-05-09T17:44:01.000Z",
  "title": "A dissipative logarithmic type evolution of second order in time",
  "authors": [
    "Fábio L. Oliveira",
    "Diego G. Santos",
    "Maria J. M. Silva",
    "Dennys J. C. Silva"
  ],
  "categories": [
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T17:44:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35B40",
      "35C20",
      "35S05"
    ],
    "keywords": [
      "dissipative logarithmic type evolution",
      "second order",
      "logarithmic-type second-order model",
      "non-local logarithmic damping mechanism",
      "spectral approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}