Analysis of a diffuse interface model of multispecies tumor growth

We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermo...

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Published inNonlinearity Vol. 30; no. 4; pp. 1639 - 1658
Main Authors Dai, Mimi, Feireisl, Eduard, Rocca, Elisabetta, Schimperna, Giulio, Schonbek, Maria E
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.04.2017
Subjects
Cahn-Hilliard equation
Darcy law
diffuse interface model
reaction-diffusion equation
singular limits
tumor growth
weak solution
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Abstract We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity u satisfies u⋅ν>0, where ν is the outer normal to the boundary of the domain.
AbstractList We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity u satisfies u⋅ν>0, where ν is the outer normal to the boundary of the domain.
Author Dai, Mimi
Feireisl, Eduard
Schimperna, Giulio
Schonbek, Maria E
Rocca, Elisabetta
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Snippet We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new...
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SubjectTerms Cahn-Hilliard equation
Darcy law
diffuse interface model
reaction-diffusion equation
singular limits
tumor growth
weak solution
Title Analysis of a diffuse interface model of multispecies tumor growth
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Volume 30
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