{
  "abstract": "We consider the classical model for small-strain thermoviscoelastic evolution in isotropic Kelvin-Voigt materials with inertia, as given by $$\\begin{cases} u_{tt} = μΔu_t + (λ+μ)\\nabla\\nabla\\cdot u_t + \\hatμΔu + (\\hatλ+\\hatμ)\\nabla\\nabla\\cdot u - B\\nablaΘ, \\\\ κΘ_t = DΔΘ+ μ|\\nabla u_t|^2 + (λ+μ)|\\mathrm{div}\\,u_t|^2 - BΘ\\,\\mathrm{div}\\,u_t. \\end{cases}$$ Recently, Winkler (arXiv:2602.05964) established global-in-time solvability for an initial value problem in smoothly bounded multi-dimensional domains $Ω$ under homogeneous Dirichlet boundary conditions for the displacement variable $u$, and homogeneous Neumann boundary conditions for the temperature $Θ$, allowing the heat capacity $κ$ to depend on $Θ$. Moreover, it was shown there that the corresponding temperature is positive a.e. in $Ω\\times(0,\\infty)$. In the present work, we strengthen this positivity result by deriving a quantitative lower bound for $Θ$. Our analysis applies to heat capacities $κ$ with power-law scaling for small arguments, precisely: either $κ(ξ)\\simξ^α$ for some $α\\ge 0$, or $κ(ξ)\\geξ$, in a suitable neighborhood of $ξ=0$. Under these structural assumptions on $κ$, we show that for every $τ>0$ and $T>τ$ there exists $c(τ,T)>0$ such that $Θ(x,t)\\ge c(τ,T)$ for a.e. $(x,t)\\inΩ\\times(τ,T)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31124",
  "author_total": 1,
  "authors": [
    {
      "name": "Torben Fricke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/64mt1087b7g15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31124",
  "fulltext_url": null,
  "id": "64mt1087b7g15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31124",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2211|Thermoelastic and Magnetoelastic Phenomena"
    ]
  ],
  "openalex": "W7223299135",
  "pdf_url": "https://arxiv.org/pdf/2610.31124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/64mt1087b7g15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative positivity properties of the temperature in multi-dimensional thermoviscoelastic systems",
  "title_text": "Quantitative positivity properties of the temperature in multi-dimensional thermoviscoelastic systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/64mt1087b7g15",
  "venue": "arXiv",
  "versions": []
}