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Mathematics > Analysis of PDEs

arXiv:1812.08872 (math)
[Submitted on 20 Dec 2018 (v1), last revised 18 Jun 2019 (this version, v2)]

Title:On the unsteady Darcy-Forchheimer-Brinkman equation in local and nonlocal tumor growth models

Authors:Marvin Fritz, Ernesto A. B. F. Lima, J. Tinsley Oden, Barbara Wohlmuth
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Abstract:A mathematical analysis of local and nonlocal phase-field models of tumor growth is presented that includes time-dependent Darcy-Forchheimer-Brinkman models of convective velocity fields and models of long-range cell interactions. A complete existence analysis is provided. In addition, a parameter-sensitivity analysis is described that quantifies the sensitivity of key quantities of interest to changes in parameter values. Two sensitivity analyses are examined; one employing statistical variances of model outputs and another employing the notion of active subspaces based on existing observational data. Remarkably, the two approaches yield very similar conclusions on sensitivity for certain quantities of interest. The work concludes with the presentation of numerical approximations of solutions of the governing equations and results of numerical experiments on tumor growth produced using finite element discretizations of the full tumor model for representative cases.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35K35, 76D07, 35A01, 35D30, 35Q92, 65C60, 65M60
Cite as: arXiv:1812.08872 [math.AP]
  (or arXiv:1812.08872v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1812.08872
Journal reference: Math. Models Methods Appl. Sci. 29 (2019) 1691-1731
Related DOI: https://doi.org/10.1142/S0218202519500325

Submission history

From: Marvin Fritz [view email]
[v1] Thu, 20 Dec 2018 22:32:27 UTC (2,191 KB)
[v2] Tue, 18 Jun 2019 20:27:25 UTC (807 KB)
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