96 citations · 490 across the 38 of their papers we have counts for
54 papers
On a system of equations arising in meteorology: Well-posedness and data assimilation
Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses…
Unconditional stability of radially symmetric steady sates of compressible viscous fluids with inflow/outflow boundary conditions
Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
We show that certain radially symmetric steady states of compressible viscous fluids in domains with inflow/outflow boundary conditions are unconditionally stable. This means that…
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…
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…
Cahn-Hillard and Keller-Segel systems as high-friction limits of Euler-Korteweg and Euler-Poisson equations
Dennis Gallenmüller, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1
We consider a combined system of Euler--Korteweg and Euler--Poisson equations with friction and exponential pressure with exponent . We show the existence of dissipative meas…
Mathematical theory of compressible magnetohydrodynamics driven by non-conservative boundary conditions
Eduard Feireisl, Piotr Gwiazda, Young-Sam Kwon +1
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solva…
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…
Time periodic motion of temperature driven compressible fluids
Eduard Feireisl, Piotr Gwiazda, Agnieszka Swierczewska-Gwiazda
We consider the Navier-Stokes-Fourier system describing the motion of a compressible viscous fluid in a container with impermeable boundary subject to time periodic heating and und…
Analysis of the generalised Aw-Rascle model
Nilasis Chaudhuri, Piotr Gwiazda, Ewelina Zatorska
We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For an arbitrary large class of initial data and the periodic domain, we prove the e…
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…
Dissipative measure-valued solutions to the Euler-Poisson equation
José A. Carrillo, Tomasz Dębiec, Piotr Gwiazda +1
We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy a…
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…
Existence and differentiability in parameter of the measure solution to a perturbed non-linear transport equation
Piotr Gwiazda, Sander C. Hille, Kamila Łyczek
We consider a perturbation in the non-linear transport equation on measures i.e. both initial condition and the solution are bounded Radon measures $\mathcal{M}(\math…
On renormalized solutions to elliptic inclusions with nonstandard growth
Anna Denkowska, Piotr Gwiazda, Piotr Kalita
We study the elliptic inclusion given in the following divergence form \begin{align*} & -\mathrm{div}\, A(x,\nabla u) \ni f\quad \mathrm{in}\quad Ω, & u=0\quad \mathrm{on}\quad \pa…
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…
Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws
Claude Bardos, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +2
We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fract…
Asymptotic behaviour of a structured population model on a space of measures
József Z. Farkas, Piotr Gwiazda, Anna Marciniak-Czochra
In this paper we consider a physiologically structured population model with distributed states at birth, formulated on the space of non-negative Radon measures. Using a characteri…
A two species hyperbolic-parabolic model of tissue growth
Piotr Gwiazda, Benoît Perthame, Agnieszka Świerczewska-Gwiazda
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a…
Renormalized solutions to parabolic equations in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
Iwona Chlebicka, Piotr Gwiazda, Anna Zatorska-Goldstein
We provide existence and uniqueness of renomalized solutions to a general nonlinear parabolic equation with merely integrable data on a Lipschitz bounded domain in .…
Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
Iwona Chlebicka, Piotr Gwiazda, Anna Zatorska-Goldstein
We study a general nonlinear parabolic equation on a Lipschitz bounded domain in , \begin{equation*} \left\{\begin{array}{l l} \partial_t u-\mathrm{div} A(t,x,\nabla…
On the Extension of Onsager's Conjecture for General Conservation Laws
Claude Bardos, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +2
The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "…
Differentiability in perturbation parameter of measure solutions to perturbed transport equation
Piotr Gwiazda, Sander C. Hille, Kamila Łyczek +1
We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differenti…