WIAS Preprint No. 2842, (2021)

Analysis of a tumor model as a multicomponent deformable porous medium


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2020 Mathematics Subject Classification

  • 35Q92 35Q35 35K57 76S05 92B05 92C37


  • Tumor model, porous medium, diffuse interface model, Cahn--Hilliard equation, reaction-diffusion equation




We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a mechanical equilibrium equation with phase-dependent elasticity coefficients. The resulting PDE system couples two Cahn--Hilliard type equations for the tumor phase and the healthy phase with a PDE linking the evolution of the interstitial fluid to the pressure of the system, a reaction-diffusion type equation for the nutrient proportion, and a quasistatic momentum balance. We prove here that the corresponding initial-boundary value problem has a solution in appropriate function spaces.

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