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- ItemAnalysis of a tumor model as a multicomponent deformable porous medium(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, JürgenWe 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.
- ItemA variational inequality for the derivative of the scalar play operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Brokate, Martin; Krejčí, PavelWe show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral.