Related papers: Homogenization of degenerate cross-diffusion syste…
In this paper we give a new proof of the homogenization result for an immiscible incompressible two-phase flow in double porosity media obtained earlier in the pioneer work by A. Bourgeat, S. Luckhaus, A. Mikeli\'c (1996) and in the paper…
We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the…
This paper deals with the homogenization of the reaction-diffusion equations in a domain containing periodically distributed holes of size $\varepsilon$, with a dynamical boundary condition of reactive-diffusive type, i.e., we consider the…
We investigate degenerate cross-diffusion equations with a rank-deficient diffusion matrix that are considered to model populations which move as to avoid spatial crowding and have recently been found to arise in a mean-field limit of…
In this paper, we systematically study weak solutions of a linear singular or degenerate parabolic equation in a mixed divergence form and nondivergence form, which arises from the linearized fast diffusion equation and the linearized…
We consider the homogenisation of a coupled reaction-diffusion process in a porous medium with evolving microstructure. A concentration-dependent reaction rate at the interface of the pores with the solid matrix induces a…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
We consider a class of cross diffusion systems with degenerate (or porous media type) diffusion which is inspired by models in mathematical biology/ecology with zero self diffusions. Known techniques for scalar equations are no longer…
We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such…
In this contribution we obtain partial $C^{0,\alpha}$-regularity for bounded solutions of a certain class of cross-diffusion systems, which are strongly coupled, degenerate quasilinear parabolic systems. Under slightly more restrictive…
We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…
We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two-phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated…
The paper deals with the homogenization of deformable porous media saturated by two-component electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena,…
We analyze the mathematical properties of a multi-species biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet-Neumann boundary conditions on a bounded domain. This model belongs to the class of…
The paper deals with homogenization problem for nonlinear elliptic and parabolic equations in a periodically perforated domain, a nonlinear Fourier boundary conditions being imposed on the perforation border. Under the assumptions that the…
In this paper, we develop a viscosity method for Homogenization of Nonlinear Parabolic Equations constrained by highly oscillating obstacles or Dirichlet data in perforated domains. The Dirichlet data on the perforated domain can be…
Homogenization method is used to analyse the equivalent behavior of transient flow of a passive solute through highly heterogeneous porous media. The flow is governed by a coupled system which includes an elliptic equation and a linear…