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arXiv · 2105.00805

Analysis of a tumor model as a multicomponent deformable porous medium

Pavel Krejci·Elisabetta Rocca·Juergen Sprekels
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Abstract

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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Pavel Krejci, Elisabetta Rocca, Juergen Sprekels. 2021-05-03. Analysis of a tumor model as a multicomponent deformable porous medium. https://arxiv.org/abs/2105.00805

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