English
Related papers

Related papers: Space-time homogenization problems for porous medi…

200 papers

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,…

Computational Physics · Physics 2019-01-25 Jana Turjanicová , Eduard Rohan , Vladimír Lukeš

In this paper, we propose a multicontinuum homogenization approach for nonlinear problems involving dynamically evolving multiscale media. The main idea of the proposed approach is that one of the fine-scale variables defines continua. It…

Numerical Analysis · Mathematics 2025-11-18 Mohammed Al-Kobaisi , Dmitry Ammosov , Yalchin Efendiev , Wing Tat Leung , Buzheng Shan

We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: {\em micro-macro}). The geometry we have in mind includes regions of…

Mathematical Physics · Physics 2010-03-23 T. van Noorden , A. Muntean

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the…

Analysis of PDEs · Mathematics 2010-02-10 Fabio Camilli , Olivier Ley , Paola Loreti

This work is devoted to the homogenization of elliptic equations in high-contrast media in the so-called 'double-porosity' resonant regime, for which we solve two open problems of the literature. First, we prove qualitative stochastic…

Analysis of PDEs · Mathematics 2025-04-07 Elise Bonhomme , Mitia Duerinckx , Antoine Gloria

Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded.…

Computational Physics · Physics 2017-03-08 Bruno Lombard , Agnes Maurel , Jean-Jacques Marigo

We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation driving source. We employ the non-equilibrium gray diffusion…

High Energy Astrophysical Phenomena · Physics 2024-11-25 Nitay Derei , Shmuel Balberg , Shay I. Heizler , Elad Steinberg , Ryan G. McClarren , Menahem Krief

In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the context of homogenized elastic properties of materials. This…

Analysis of PDEs · Mathematics 2023-07-10 Virginie Ehrlacher , Frederic Legoll , Benjamin Stamm , Shuyang Xiang

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…

Numerical Analysis · Mathematics 2025-07-09 Yulei Liao , Pingbing Ming

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…

Biological Physics · Physics 2019-01-31 Elliot J. Carr , Matthew J. Simpson

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…

Fluid Dynamics · Physics 2024-10-16 Lucy C Auton , Mohit P. Dalwadi , Ian M. Griffiths

The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence…

Analysis of PDEs · Mathematics 2021-12-07 Abdelhamid Ainouz

In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale…

Numerical Analysis · Mathematics 2019-09-04 Wing T. Leung , Eric T. Chung , Yalchin Efendiev , Maria Vasilyeva , Mary Wheeler

For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved…

Mathematical Physics · Physics 2015-01-30 Vladimir Maz'ya , Alexander Movchan , Michael Nieves

We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of $L^{q}$-weak solutions (satisfying energy estimates or even further with moment and speed estimates in Wasserstein spaces),…

Analysis of PDEs · Mathematics 2023-03-07 Sukjung Hwang , Kyungkeun Kang , Haw Kil Kim

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

Numerical Analysis · Mathematics 2018-12-27 Robert Altmann , Eric Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

In this paper we develop homogenization theory for spatiotemporally modulated wire medium. We first solve for the modal waves that are supported by this composite medium, we show peculiar properties such as extraordinary waves that…

Applied Physics · Physics 2021-11-18 Michael Kreiczer , Yakir Hadad

In this paper we consider the homogenization problem of nonlinear evolution equations with space-time non-locality, the problems are given by Beltritti and Rossi [JMAA, 2017, 455: 1470-1504]. When the integral kernel $J(x,t;y,s)$ is…

Analysis of PDEs · Mathematics 2023-10-31 Junlong Chen , Yanbin Tang

In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…

Probability · Mathematics 2018-10-18 Hakima Bessaih , Yalchin Efendiev , Razvan Florian Maris

We study weighted porous media equations on domains $\Omega\subseteq{\mathbb R}^N$, either with Dirichlet or with Neumann homogeneous boundary conditions when $\Omega\not={\mathbb R}^N$. Existence of weak solutions and uniqueness in a…

Analysis of PDEs · Mathematics 2012-11-09 Gabriele Grillo , Matteo Muratori , Maria Michaela Porzio