We propose a diffuse interface model to describe a 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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Pavel Krejčí, Elisabetta Rocca, Jürgen Sprekels, Analysis of a tumor model as a multicomponent deformable porous medium. Interfaces Free Bound. 24 (2022), no. 2, pp. 235–262DOI 10.4171/IFB/472