A. Jüngel, Ines Stelzer:

"Entropy structure of a cross-diffusion tumor-growth model";

Mathematical Models & Methods in Applied Sciences,22(2012), S. 1 - 26.

Siehe englisches Abstract.

The mechanical tumor-growth model of Jackson and Byrne is analyzed. The model

consists of nonlinear parabolic cross-diffusion equations in one space dimension for the

volume fractions of the tumor cells and the extracellular matrix (ECM). It describes

tumor encapsulation influenced by a cell-induced pressure coefficient. The global-in-time

existence of bounded weak solutions to the initial-boundary-value problem is proved

when the cell-induced pressure coefficient is smaller than a certain explicit critical value.

Moreover, when the production rates vanish, the volume fractions converge exponentially

fast to the homogeneous steady state. The proofs are based on the existence of entropy

variables, which allows for a proof of the non-negativity and boundedness of the volume

fractions, and of an entropy functional, which yields gradient estimates and provides a

new thermodynamic structure. Numerical experiments using the entropy formulation of

the model indicate that the solutions exist globally in time also for cell-induced pressure

coefficients larger than the critical value. For such coefficients, a peak in the ECM volume

fraction forms and the entropy production density can be locally negative.

Tumor growth; encapsulation; cross diffusion

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.