---
OA_place: publisher
OA_type: hybrid
_id: '19783'
abstract:
- lang: eng
  text: We consider a local Cahn–Hilliard‐type model for tumor growth as well as a
    nonlocal model where, compared to the local system, the Laplacian in the equation
    for the chemical potential is replaced by a nonlocal operator. The latter is defined
    as a convolution integral with suitable kernels parametrized by a small parameter.
    For sufficiently smooth bounded domains in three dimensions, we prove convergence
    of weak solutions of the nonlocal model toward strong solutions of the local model
    together with convergence rates with respect to the small parameter. The proof
    is done via a Gronwall‐type argument and a convergence result with rates for the
    nonlocal integral operator toward the Laplacian due to Abels and Hurm.
acknowledgement: C. Hurm was partially supported by the Graduiertenkolleg 2339 IntComSin
  of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)–Project-ID
  321821685. M. Moser has received funding from the European Research Council (ERC)
  under the European Union's Horizon 2020 research and innovation programme (grant
  agreement No 948819). The support is gratefully acknowledged. Finally, we thank
  Daniel Böhme and Jonas Stange for careful proofreading. Open Access funding enabled
  and organized by Projekt DEAL.
article_number: e70003
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Christoph
  full_name: Hurm, Christoph
  last_name: Hurm
- first_name: Maximilian
  full_name: Moser, Maximilian
  id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
  last_name: Moser
citation:
  ama: Hurm C, Moser M. Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth
    model. <i>GAMM-Mitteilungen</i>. 2025;48(2). doi:<a href="https://doi.org/10.1002/gamm.70003">10.1002/gamm.70003</a>
  apa: Hurm, C., &#38; Moser, M. (2025). Nonlocal‐to‐local convergence for a Cahn–Hilliard
    tumor growth model. <i>GAMM-Mitteilungen</i>. Wiley. <a href="https://doi.org/10.1002/gamm.70003">https://doi.org/10.1002/gamm.70003</a>
  chicago: Hurm, Christoph, and Maximilian Moser. “Nonlocal‐to‐local Convergence for
    a Cahn–Hilliard Tumor Growth Model.” <i>GAMM-Mitteilungen</i>. Wiley, 2025. <a
    href="https://doi.org/10.1002/gamm.70003">https://doi.org/10.1002/gamm.70003</a>.
  ieee: C. Hurm and M. Moser, “Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor
    growth model,” <i>GAMM-Mitteilungen</i>, vol. 48, no. 2. Wiley, 2025.
  ista: Hurm C, Moser M. 2025. Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor
    growth model. GAMM-Mitteilungen. 48(2), e70003.
  mla: Hurm, Christoph, and Maximilian Moser. “Nonlocal‐to‐local Convergence for a
    Cahn–Hilliard Tumor Growth Model.” <i>GAMM-Mitteilungen</i>, vol. 48, no. 2, e70003,
    Wiley, 2025, doi:<a href="https://doi.org/10.1002/gamm.70003">10.1002/gamm.70003</a>.
  short: C. Hurm, M. Moser, GAMM-Mitteilungen 48 (2025).
date_created: 2025-06-03T08:58:01Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2025-06-03T09:14:17Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1002/gamm.70003
ec_funded: 1
external_id:
  arxiv:
  - '2402.13790'
file:
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  creator: dernst
  date_created: 2025-06-03T09:12:22Z
  date_updated: 2025-06-03T09:12:22Z
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file_date_updated: 2025-06-03T09:12:22Z
has_accepted_license: '1'
intvolume: '        48'
issue: '2'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
  call_identifier: H2020
  grant_number: '948819'
  name: Bridging Scales in Random Materials
publication: GAMM-Mitteilungen
publication_identifier:
  eissn:
  - 1522-2608
  issn:
  - 0936-7195
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2025'
...