Geodesic
Analysis of a tumor model as a multicomponent deformable porous medium
Pavel Krejcí1 ; Elisabetta Rocca2 ; Jürgen Sprekels3
1Czech Technical University, Prague, Czech Republic
2Università degli Studi di Pavia, Italy
3Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 235-262

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DOI

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.
DOI : 10.4171/ifb/472
Classification : 76-XX, 74-XX
Mots-clés : Tumor model, porous medium, diffuse interface model, Cahn–Hilliard equation, reaction-diffusion equation

Pavel Krejcí  1   ; Elisabetta Rocca  2   ; Jürgen Sprekels  3

1 Czech Technical University, Prague, Czech Republic
2 Università degli Studi di Pavia, Italy
3 Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany 
Pavel Krejcí; Elisabetta Rocca; Jürgen Sprekels. Analysis of a tumor model as a multicomponent deformable porous medium. Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 235-262. doi: 10.4171/ifb/472
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     title = {Analysis of a tumor model as a multicomponent deformable porous medium},
     journal = {Interfaces and free boundaries},
     pages = {235--262},
     year = {2022},
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     number = {2},
     doi = {10.4171/ifb/472},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/472/}
}
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