96 citations · 490 across the 38 of their papers we have counts for
9 papers · 1 filter
Conservation of energy for the Euler-Korteweg equations
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the…
Gossez's approximation theorems in the Musielak-Orlicz-Sobolev spaces
Youssef Ahmida, Iwona Chlebicka, Piotr Gwiazda +1
We prove the density of smooth functions in the modular topology in the Musielak-Orlicz-Sobolev spaces essentially extending the results of Gossez \cite{GJP2} obtained in the Orlic…
Relative entropy method for measure-valued solutions in natural sciences
Tomasz Dębiec, Piotr Gwiazda, Kamila Łyczek +1
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the n…
A tribute to conservation of energy for weak solutions
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolu…
Existence of global weak solutions to the kinetic Peterlin model
Piotr Gwiazda, Mária Lukáčová-Medviďová, Hana Mizerová +1
We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely ex…
Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak-Orlicz spaces in the class of renormalized solutions
Iwona Chlebicka, Piotr Gwiazda, Anna Zatorska-Goldstein
We prove existence and uniqueness of renormalized solutions to general nonlinear parabolic equation in Musielak-Orlicz space avoiding growth restrictions. Namely, we consider \[\pa…
A note on weak solutions of conservation laws and energy/entropy conservation
Piotr Gwiazda, Martin Michálek, Agnieszka Świerczewska-Gwiazda
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second l…
Homogenization of nonlinear elliptic systems in nonreflexive Musielak-Orlicz spaces
Miroslav Bulíček, Piotr Gwiazda, Martin Kalousek +1
We study the homogenization process for families of strongly nonlinear elliptic systems with the homogeneous Dirichlet boundary conditions. The growth and the coercivity of the ell…
Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space
Piotr Gwiazda, Iwona Skrzypczak, Anna Zatorska-Goldstein
We prove existence of renormalized solutions to general nonlinear elliptic equation in Musielak-Orlicz space avoiding growth restrictions. Namely, we consider \begin{equation*} -{\…