21 citations · 34 across the 16 of their papers we have counts for
17 papers
Nonlocal-to-local convergence of the Cahn-Hilliard equation with degenerate mobility and the Flory-Huggins potential
Charles Elbar, Jakub Skrzeczkowski
The Cahn-Hilliard equation is a fundamental model for phase separation phenomena. Its rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link in…
On the limit problem arising in the kinetic derivation of the Cahn-Hilliard equation
Charles Elbar, Benoît Perthame, Jakub Skrzeczkowski
The non-local degenerate Cahn-Hilliard equation is derived from the Vlasov equation with long-range attraction. We study the local limit as the delocalization parameter converges t…
On the rate of convergence of Yosida approximation for the nonlocal Cahn-Hilliard equation
Piotr Gwiazda, Jakub Skrzeczkowski, Lara Trussardi
It is well-known that one can construct solutions to the nonlocal Cahn-Hilliard equation with singular potentials via Yosida approximation with parameter . The usual method…
On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure
Charles Elbar, Jakub Skrzeczkowski
Several recent papers have addressed modelling of the tissue growth by the multi-phase models where the velocity is related to the pressure by one of the physical laws (Stoke's, Br…
Nonlocal Cahn-Hilliard equation with degenerate mobility: Incompressible limit and convergence to stationary states
Charles Elbar, Benoît Perthame, Andrea Poiatti +1
The link between compressible models of tissue growth and the Hele-Shaw free boundary problem of fluid mechanics has recently attracted a lot of attention. In most of these models,…
From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit
Charles Elbar, Piotr Gwiazda, Jakub Skrzeczkowski +1
Several recent papers considered the high-friction limit for systems arising in fluid mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard equation a…
Degenerate Cahn-Hilliard systems: From nonlocal to local
José A. Carrillo, Charles Elbar, Jakub Skrzeczkowski
We provide a rigorous mathematical framework to establish the limit of a nonlocal model of cell-cell adhesion system to a local model. When the parameter of the nonlocality goes to…
Non-Newtonian fluids with discontinuous-in-time stress tensor
Miroslav Buliček, Piotr Gwiazda, Jakub Skrzeczkowski +1
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and ha…
Degenerate Cahn-Hilliard equation: From nonlocal to local
Charles Elbar, Jakub Skrzeczkowski
There has been recently an important interest in deriving rigorously the Cahn-Hilliard equation from the nonlocal equation, also called aggregation equation. So far, only non-degen…
From Vlasov equation to degenerate nonlocal Cahn-Hilliard equation
Charles Elbar, Marco Mason, Benoît Perthame +1
We provide a rigorous mathematical framework to establish the hydrodynamic limit of the Vlasov model introduced by Noguchi and Takata in order to describe phase transition of fluid…
Pressure jump and radial stationary solutions of the degenerate Cahn-Hilliard equation
Charles Elbar, Benoît Perthame, Jakub Skrzeczkowski
The Cahn-Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues. We are interested in quantifying the pressure jump at the int…
On a range of exponents for absence of Lavrentiev phenomenon for double phase functionals
Miroslav Bulíček, Piotr Gwiazda, Jakub Skrzeczkowski
For a class of functionals having the -growth, we establish an improved range of exponents , for which the Lavrentiev phenomenon does not occur. The proof is based on…
Measure Differential Equation with a Nonlinear Growth/Decay Term
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of appr…
Convergence of the EBT method for a non-local model of cell proliferation with discontinuous interaction kernel
Piotr Gwiazda, Błażej Miasojedow, Jakub Skrzeczkowski +1
We consider the EBT algorithm (a particle method) for the non-local equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel w…
Bayesian inference of a non-local proliferation model
Zuzanna Szymańska, Jakub Skrzeczkowski, Błażej Miasojedow +1
From a systems biology perspective the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that t…
Fast reaction limit with nonmonotone reaction function
Benoît Perthame, Jakub Skrzeczkowski
We analyse fast reaction limit in the reaction-diffusion system with nonmonotone reaction function and one non-diffusing component. As speed of reaction tends to infinity, the conc…
Parabolic equations in Musielak -- Orlicz spaces with discontinuous in time -function
Miroslav Bulíček, Piotr Gwiazda, Jakub Skrzeczkowski
We consider a parabolic PDE with Dirichlet boundary condition and monotone operator with non-standard growth controlled by an -function depending on time and spatial variabl…