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Related papers: Weak Solutions for a Poro-elastic Plate System

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We consider the three-dimensional fluid-structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper boundary. The fluid is described by the incompressible…

Analysis of PDEs · Mathematics 2025-12-12 Mario Bukal , Igor Kukavica , Linfeng Li , Boris Muha

In this paper we deduce by {\Gamma}-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we study the case…

Analysis of PDEs · Mathematics 2013-05-03 Elisa Davoli

We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2026-05-01 Helmut Abels , Jonas Haselböck

We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary…

Analysis of PDEs · Mathematics 2020-07-14 Miroslav Bulíček , Josef Málek , Vít Průša , Endre Süli

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Analysis of PDEs · Mathematics 2026-01-13 Bohan Ouyang , Maurizio Grasselli , Hao Wu

In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show…

Analysis of PDEs · Mathematics 2022-01-12 B. Benesova , M. Kampschulte , S. Schwarzacher

The aim of the present study is to derive the effective quasi-static behaviour of a composite medium, made of a poroelastic matrix containing elastic impervious inclusions. For this purpose, the asymptotic homogenisation method is used. On…

Soft Condensed Matter · Physics 2019-02-15 Pascale Royer , Pierre Recho , Claude Verdier

Euler alignment systems appear as hydrodynamic limits of interacting self-propelled particle systems such as the (generalized) Cucker-Smale model. In this work, we study weak solutions to an Euler alignment system on smooth, bounded,…

Analysis of PDEs · Mathematics 2023-05-24 Amoolya Tirumalai , Christos Mavridis , John S. Baras

We consider the fully dynamic Biot-Allard model, which includes memory effects. Convolution integrals in time model the history of the porous medium. We use a series representation of the dynamic permeability in the frequency domain to…

Analysis of PDEs · Mathematics 2024-06-04 Jakob S. Stokke , Markus Bause , Nils Margenberg , Florin A. Radu

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…

Analysis of PDEs · Mathematics 2017-01-03 Helmut Abels , Dominic Breit

The aim of this paper is to prove global in time existence of weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobilities. Our model couples the diffusive interface model with…

Analysis of PDEs · Mathematics 2022-08-31 Aaron Brunk , Maria Lukacova-Medvidova

This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…

Analysis of PDEs · Mathematics 2024-02-13 Roman M. Taranets , Hangjie Ji , Marina Chugunova

We consider port-Hamiltonian systems from a geometric perspective, where the quantities involved such as state, flows, and efforts evolve in (possibly infinite-dimensional) Banach spaces. The main contribution of this article is the…

Dynamical Systems · Mathematics 2025-09-09 Timo Reis

We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear…

Numerical Analysis · Mathematics 2019-02-05 Ilona Ambartsumyan , Vincent J. Ervin , Truong Nguyen , Ivan Yotov

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the…

Analysis of PDEs · Mathematics 2020-02-04 Jingning He

The uniqueness of global weak solutions to one-dimensional doubly degenerate cross-diffusion system is shown. The equations model the evolution of feeding bacterial populations in a malnourished environment. The key idea of the proof is…

Analysis of PDEs · Mathematics 2025-01-14 Xiuqing Chen , Bang Du

Multiphase poromechanics describes the evolution of multiphase flow in deformable porous media. Mathematical models for such multiphysics system are inheritely nonlinear, potentially degenerate and fully coupled systems of partial…

Analysis of PDEs · Mathematics 2023-12-05 Jakub Wiktor Both , Clément Cancès

Biot's equations of poroelasticity contain a parabolic system for the evolution of the pressure, which is coupled with a quasi-stationary equation for the stress tensor. Thus, it is natural to extend the existing work on isogeometric…

Numerical Analysis · Mathematics 2021-02-17 Jeremias Arf , Bernd Simeon

This study proposes and explores a linear hydrodynamic thermo-elasticity system within mixture models, comprising fluid and solid phases, with a focus on biological tissues, particularly tumor-related phenomena. Although tumor growth is not…

Analysis of PDEs · Mathematics 2025-02-11 Michael Eden , Meraj Alam , Prakash Kumar , G P Raja Sekhar

In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…

Analysis of PDEs · Mathematics 2023-10-23 Abramo Agosti , Robert Lasarzik , Elisabetta Rocca