{
  "abstract": "We analyze solutions to a one-dimensional periodic linear model for peridynamic waves, focusing on the setting where the natural energy space allows for spatial discontinuities. Exploiting the high-frequency asymptotics of the peridynamic dispersion relation, we construct an explicit solution whose initial displacement has a single jump discontinuity but becomes continuous at every positive time. By time reversibility, this yields a continuous initial displacement whose evolution develops a jump at any prescribed time and is continuous at every other time. We further quantify the formation of this singularity through a sharp Hölder-norm blow-up estimate obtained via a Littlewood-Paley characterization of Hölder spaces. Finally, by superposing suitably weighted solutions, we construct an evolution exhibiting jump discontinuities on a dense set of times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30041",
  "author_total": 5,
  "authors": [
    {
      "name": "Giuseppe Maria Coclite"
    },
    {
      "name": "Serena Dipierro"
    },
    {
      "name": "Francesco Maddalena"
    },
    {
      "name": "Gianluca Orlando"
    },
    {
      "name": "Enrico Valdinoci"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b6awc0ptwv2vd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30041",
  "fulltext_url": null,
  "id": "b6awc0ptwv2vd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30041",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7214397691",
  "pdf_url": "https://arxiv.org/pdf/2609.30041",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b6awc0ptwv2vd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30041",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30041"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dissolution and nucleation of jump discontinuities for one-dimensional periodic peridynamic waves",
  "title_text": "Dissolution and nucleation of jump discontinuities for one-dimensional periodic peridynamic waves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/b6awc0ptwv2vd",
  "venue": "arXiv",
  "versions": []
}