{
  "abstract": "In this note we study the regularity properties of the \\emph{Effort Function $E(β)$}. This can be defined as the minimal $L^1$-norm of the control $\\tilde α(x) \\geq 0$ so that the PDE $$U_t = ΔU + f(U) - \\tilde α(t,x) U, \\quad U \\in [0,1], %\\ \\tilde α\\geq 0,$$ admits a traveling profile $U(x - βt)$ connecting $0$ to $1$. The above PDE models the evolution of an invasive species, where the control $\\tilde α(t,x)$ describes the percentage amount of species removal. In the literature some conditions are assumed on the properties of $f(U)$ and (consequently) on the effort function $E(β)$, the main ones being that the traveling profile has a simple structure and that the effort function can be used as an anisotropic perimeter to generated a cost function over sets of finite perimeter. This note gives some examples showing that in the interesting cases, i.e. when the PDE has a non trivial dynamics, these assumptions are in general not satisfied. We also show that $E(β)$ is in general only $C^1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11604",
  "author_total": 2,
  "authors": [
    {
      "name": "Stefano Bianchini"
    },
    {
      "name": "Chiara Trifone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/811rem2r9wxqf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11604",
  "fulltext_url": null,
  "id": "811rem2r9wxqf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11604",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221082508",
  "pdf_url": "https://arxiv.org/pdf/2610.11604",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/811rem2r9wxqf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11604",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11604"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Some counterexamples concerning a model of eradication of invasive species",
  "title_text": "Some counterexamples concerning a model of eradication of invasive species",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/811rem2r9wxqf",
  "venue": "arXiv",
  "versions": []
}