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Analysis of linearized elasticity models with point sources in weighted Sobolev spaces: applications in tissue contraction.

  • Published In: ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN), 2023, v. 57, n. 4. P. 2349 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Boon, Wietse M.; Vermolen, Fred J. 3 of 3

Abstract

In order to model the contractive forces exerted by fibroblast cells in dermal tissue, we propose and analyze two modeling approaches under the assumption of linearized elasticity. The first approach introduces a collection of point forces on the boundary of the fibroblast whereas the second approach employs an isotropic stress point source in its center. We analyze the resulting partial differential equations in terms of weighted Sobolev spaces and identify the singular behavior of the respective solutions. Two finite element method approaches are proposed, one based on a direct application and another in which the singularity is subtracted and a correction field is computed. Finally, we confirm the validity of the modeling approach, demonstrate convergence of the numerical methods, and verify the analysis through the use of numerical experiments. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN). 2023/07, Vol. 57, Issue 4, p2349
  • Document Type:Article
  • Subject Area:Law
  • Publication Date:2023
  • ISSN:2822-7840
  • DOI:10.1051/m2an/2023055
  • Accession Number:173707883
  • Copyright Statement:Copyright of ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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