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Author: Krejčí, Pavel × Author: Rocca, Elisabetta × Author: Sprekels, Jürgen × Type: Text ×

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Now showing 1 - 3 of 3
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    A nonlocal phase-field model with nonconstant specific heat
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen
    We prove the existence, uniqueness, thermodynamic consistency, global boundedness from both above and below, and continuous data dependence for a strong solution to an integrodifferential model for nonisothermal phase transitions under nonhomogeneous mixed boundary conditions. The specific heat is allowed to depend on the order parameter, and the convex component of the free energy may or may not be singular.
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    Analysis of a tumor model as a multicomponent deformable porous medium
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen
    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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    Unsaturated deformable porous media flow with phase transition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen
    In the present paper, a continuum model is introduced for fluid flow in a deformable porous medium, where the fluid may undergo phase transitions. Typically, such problems arise in modeling liquid-solid phase transformations in groundwater flows. The system of equations is derived here from the conservation principles for mass, momentum, and energy and from the Clausius-Duhem inequality for entropy. It couples the evolution of the displacement in the matrix material, of the capillary pressure, of the absolute temperature, and of the phase fraction. Mathematical results are proved under the additional hypothesis that inertia effects and shear stresses can be neglected. For the resulting highly nonlinear system of two PDEs, one ODE and one ordinary differential inclusion with natural initial and boundary conditions, existence of global in time solutions is proved by means of cut-off techniques and suitable Moser-type estimates.