Analysis of a tumor model as a multicomponent deformable porous medium
- Krejčí, Pavel
- Rocca, Elisabetta
- Sprekels, Jürgen
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.
- Interfaces Free Bound., 24 (2022), pp. 235--262, DOI 10.4171/IFB/472 .