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Related papers: Degenerate diffusion with Preisach hysteresis

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We study the well-posedness of a modified degenerate Cahn-Hilliard type model for surface diffusion. With degenerate phase-dependent diffusion mobility and additional stabilizing function, this model is able to give the correct sharp…

Analysis of PDEs · Mathematics 2022-04-19 Xiaohua Niu , Yang Xiang , Xiaodong Yan

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

It is shown that the problem of moisture propagation in porous media with a nonlinear relation between the mass flux and the pressure gradient as a counterpart of the Darcy law exhibits the property of bounded speed of propagation even in…

Analysis of PDEs · Mathematics 2025-05-27 Chiara Gavioli , Pavel Krejčí

We study the existence and infinite-speed propagation of solutions to models arising in porous media, when the mobility is highly degenerate (inverse power law). The approach is based on maximum principles for the fractional Laplacian, and…

Analysis of PDEs · Mathematics 2025-11-21 Antonin Chodron de Courcel

We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…

Analysis of PDEs · Mathematics 2024-08-15 Helmut Abels , Harald Garcke , Andrea Poiatti

Dense particulate suspensions often become more dilute as they move downstream through a constriction. We find that as a shear-thickening suspension is extruded through a narrow die and undergoes such liquid migration, the extrudate…

Soft Condensed Matter · Physics 2019-09-25 Rory E. O'Neill , John R. Royer , Wilson C. K. Poon

Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and…

Analysis of PDEs · Mathematics 2024-10-18 Maria Eckardt , Anna Zhigun

In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…

Analysis of PDEs · Mathematics 2016-09-16 Christian Heinemann , Christiane Kraus

A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…

Analysis of PDEs · Mathematics 2026-03-12 Saumyajit Das , Ram Gopal Jaiswal

The occurrence of heterogeneous perturbations of fluid mass density and solid elastic strain of a porous continuum, as a consequence of its undrained response is a very important topic in theoretical and applied poromechanics. The classical…

Mathematical Physics · Physics 2017-03-03 P. Artale Harris , E. N. M. Cirillo , G. Sciarra

A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence…

Numerical Analysis · Mathematics 2015-03-18 Mostafa Bendahmane , Ziad Khalil , Mazen Saad

The principle of virtual power is used to derive the equilibrium field equations of a porous solid saturated with a fluid, including second density-gradient effects; the intention is the elucidation and extension of the effective stress…

Mathematical Physics · Physics 2010-07-14 F. dell'isola , M. Guarascio , K. Hutter

Various degenerate diffusion equations exhibit a waiting time phenomenon: Dependening on the "flatness" of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount…

Analysis of PDEs · Mathematics 2019-11-12 Julian Fischer , Daniel Matthes

The problem of the diffusion evolution of a pore filled with molecular hydrogen in a spherical granule in a hydrogen medium is solved. The initial position of the pore is displaced relative to the center of the granule. A nonlinear system…

Mesoscale and Nanoscale Physics · Physics 2022-03-31 M. I. Kopp , P. N. Ostapchuk , V. V. Yanovsky

Vapor adsorption experiments are widely used to assess pore size distributions, but the large hysteresis sometimes observed between sorption and desorption isotherms remains difficult to interpret. Such hysteresis is influenced pore network…

Materials Science · Physics 2018-07-03 Matthew B. Pinson , Tingtao Zhou , Hamlin M. Jennings , Martin Z. Bazant

We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the…

We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…

Numerical Analysis · Mathematics 2022-07-20 Mirjana Brdar , Sebastian Franz , Lars Ludwig , Hans-Görg Roos

A finite element method with mass-lumping and flux upwinding, is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary…

Numerical Analysis · Mathematics 2020-01-27 Girault Vivette , Riviere Beatrice , Cappanera Loic

We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or…

Fluid Dynamics · Physics 2023-11-21 Brian Straughan , Antonio Barletta

We introduce a notion of viscosity solutions for a nonlinear degenerate diffusion equation with a drift potential. We show that our notion of solutions coincide with the weak solutions defined via integration by parts. As an application of…

Analysis of PDEs · Mathematics 2009-10-20 I. C. Kim , H. K. Lei